First off, I’d like to start this post by saying that GRRM was asked this very question. He responded by saying that it was magic and will be revealed at the end of the series – rational, scientific explanations would not help.
Speculations are rampant, of course, but there was reportedly a blurb on the first editions of Game of Thrones that read, “long ago, the seasons were thrown out of balance by a preternatural event“. This seems to signify that the planet did have regular seasons once upon a time, and might revert to this cycle by the end of the series. This makes sense, because, how else could the people of this world celebrate name days and know the beginning of each new year (in all probability, a year is longer than 365 days on the planet, especially taking into consideration the quick maturing of teens)? Besides, with such violent climate fluctuations, it would have been highly improbable that intelligent life began on a planet.
There are many theories as to how the seasons came to be this way. One theory is that magic became so powerful with the Children of the Forest, they could exercise power on bodies outside the planet. A favorite story is that of the Hammer of the Waters that was called down to break the Arm of Dorne during invasion of Westeros by the First Men, causing the entire landmass to be split into two continents. This hammer could have been an asteroid summoned to the planet, destroying the bridge. One other story about an asteroid -rather, a moon- is the Qartheen legend that talks about how dragons were brought to earth by a second moon that exploded when it traveled too close to the sun. The two celestial objects could actually have been the same one, although highly improbable.
The first time we hear about erratic seasons is during the Long Night, almost 8,000 years ago, before the construction of the Wall. The Others / White Walkers invaded Westeros and killed almost all men during this period of cold and darkness that lasted a hundred years. This particular event, coupled with the creation of the Wall and rise of the Others (Ice Magic), along with the rise of Valyria and the dragons (Fire Magic) might actually be the onset of the shifting pattern in the seasons as well. It is said that when the last dragon died, the summers became shorter and the winters became longer. It’s almost as if the long summers and longer winters are battles played out by R’hllor and the Great Other. It’s quite possible that once the Great Other -if at all he exists- is defeated, the White Walkers are destroyed, the Wall comes down, and dragons leave the earth again, the seasons would be restored to normal – when the ice and fire magic comes to a balance.
However, we do know that the seasons are crazy out of whack, and for the purposes of this question, let’s talk about the abundant possibilities that try to offer scientific explanation as to how such seasonal phenomena can be sustained:
Water Currents and Winds
Winds affect the weather on earth to a large extent (not the seasons). Affected regions can have a temporary climatic change, affecting the onset of seasons. Global wind belts have unique behavior that maintain the heat balance caused by change in seasons. Warm winds rise up north, while cold winds batter Australia. Fluctuations in these winds can cause depressions, resulting in tornadoes and storms – common occurrences we are well aware of. Santa Ana winds are a great example. They are either hot or cold, depending on the season. But they definitely cause a fluctuation in the weather. They make California rather extremely hot when they come, and also cause a lot of forest fires. The bora winds caused a dip of 14 degrees in Croatia last year, freezing water inside of pipes.  Chinook winds probably have the most impressive of weather changing powers in Canada – warm winds can make snow a foot deep disappear in less than a day, and cold winds can change the temperature of the Prairies by over 20 degrees celcius. The winds have known to change the weather from below -20°C (-4°F) to as high as 10-20°C (50-68°F) for a few days! 
Water currents have a significantly stronger impact on the climate of a geographic location, stalling the change of seasons. The La Niña–El Niño cycle is a great example. The La Niña ocean current lowers the temperature of the Atlantic by a good 3 – 5 °C. In the United States, an episode of La Niña is defined as a period of at least 5 months. El Niño brings about rise in temperatures that last up to nine months. Anything longer is classified as an episode, and can last up to five years. These winds typically bring about hurricane seasons, with a dramatic increase in the number of hurricanes and typhoons throughout the world.
(La Niña projections for 2010-2011 season. More images can be found here: 4. El Niño and La Niña processes and their effects on Africa’s climate)
These winds and water currents depend largely on the geography of the planet. The world of ASOIAF needs to have very large mountains and even larger water bodies for currents to affect the weather long term and bring seasons that last years. We know that the Land of Always Winter, beyond the Wall is the size of Canada. This makes up for just about 1/6th the size of Westeros. That’s a lot of land. Essos is almost twice or thrice the size of Westeros, depending on who you ask, as is Sothoryos. There’s yet another landmass, Ulthos, that we haven’t even see on the map. Presumably, it’s on the other side. We do know that it’s smaller than Essos, so the water body needs to be unbelievably huge and prone to mega cyclones.
We can safely assume that while the winds and water currents may not create these seasons, they definitely plays a major part in the lengthening the periods of each season.
Massive Global Warming brought about by the Doom of Valyria
Out of jack seasons are a common side-effect of a bad case of serious global warming. The long winters seem to indicate that each one is a tiny ice age. The Doom of Valyria was a cataclysmic even that created a tsunami powerful enough to break Valyria into multiple small islands. Between the islands was created the Smoking Sea, which we assume is water at extremely high temperatures. The entire Freehold was annihilated in a single night of fire and storm, with great earthquakes and volcanic eruptions destroying everything.
Tyrion talks of the event thus:
It was written that on the day of Doom every hill for 500 miles had split asunder to fill the air with ash and smoke and fire, blazes so hot and hungry that even dragons in the sky were engulfed and consumed. Great rents had opened in the earth, swallowing palaces, temples, entire towns. Lakes boiled or turned to acid, mountains burst, fiery fountains spewed molten rock a thousand feet into the air, red clouds rained down dragonglass and the black blood of demons, and to the north the ground splintered and collapsed and fell in on itself and an angry sea came rushing in.
This definitely sounds like something capable of destroying dinosaurs and bringing about an ice age, causing large scale climate change.
Axial Tilt of the Planet
We know that there is a tilt because, a) there are seasons, and b) Essos is more in the south than Westeros, and is warmer.
Earth’s axial tilt is constant at 23.4 degrees. This is what causes seasons – during summer in the Northern hemisphere, the northern part of our planet faces the sun, while during winters, the southern part faces the sun. Ergo, Australia celebrates Christmas during summer.
The moon plays a huge part in keeping the axis of our earth stable. It’s quite possible, if going with the second moon legend, that the alternate Earth in the ASOIAF world had two moons that kept the tilt from getting wobbly. One of the moons, due to some catastrophic event, managed to get destroyed, spewing the world with dragons (and possibly White Walkers), leaving the planet with just one moon incapable of keeping the tilt stable. With a wobbly tilt, there is a huge chance of having seasons that extend for years.
The Maesters at the Citadel sure do study complicated sciences. They have a link for Astronomy in their chain, I believe. They consult for long periods of time with each other before sending out ravens that herald the change of seasons.
SPOILER: Now that Sam is in the Citadel, we might find out if the second moon actually has a basis in truth.
If the second moon theory proves to be true, the coming of the Red Comet might actually be the onset of the tilt stabilization.
However, the eye of the Ice Dragon constellation always points north, so I guess the wobbly axis theory is all but ruled out.
The planet could be orbiting around a binary star system. One of the stars could be a regular yellow dwarf like our sun, and the other, a much lighter brown dwarf. The only practical way a planet can orbit a binary star system is if its orbit lies outside of the two stars’ orbits (the two stars have their own orbits in a binary system). Such a planet would be quite huge, and in all probability, extrasolar, i.e, orbiting outside the solar system . I believe all of the known circumbinary planets are about the size of Jupiter.
This might cause the planetary orbit to be extremely elongated with a high eccentricity. This could cause the seasons’ lengths to be erratic. But they would still be pretty regular, IMO.
What’s the weather like in Tatooine?
Figure Eight Orbit
Three bodies of equal mass can theoretically exert gravitational pull on each other.  This is allowed by General Relativity.
Here, we can have each of the bodies orbiting around the other two, in an 8 shaped orbit. This would cause some pretty strange weather phenomenon. Such a system has not been discovered yet, although it’s probability of existence is not zero. We can also presume that a single planet can revolve around two stars in an 8 pattern, like an interplanetary space flight path. When it reaches the point of center of gravity of the system or comes close to one star, weird weather changes take place. This can definitely explain summer snows, spirit summers, and false springs. This would also alter the length of days and nights, as mentioned in the series.
However, one of the stars has to be a black hole or pretty weak for this system to work, seeing as the characters only ever speak of one sun.
Secondary Star around the Planet
The planet could be revolving around a primary star, while a much smaller, secondary star revolves around the primary as well.
This system would work, provided the orbit of the planet has high eccentricity (extremely elliptical) due to the pull from the second star. However, this requires the primary to be powerful enough so as to keep the secondary in orbit around itself, and the secondary to be weak enough so as to not pull the planet away from the primary. And a satellite might be hard to retain. A contradiction of sorts.
Influence of Neighboring Planets
A near impossible, far-fetched theory where our planet’s orbit is constantly affected by the other planets around it, that pull and push it around. This system has to be stable with the forces of all planets compensating for changes in each others’ orbits because without stability, there’s a high possibility of ASOIAF’s planet getting pulled too close and ultimately crashing into a bigger planet.
There exist rogue planets, also known as floating planets or orphan planets in the Universe that revolve around galaxies directly, without belonging to any solar system. These planets are usually ejected out of their birth solar systems, or have never been a part of one.
A number of obvious questions rise, which have all been explained by science : a hydrogen rich atmosphere would retain heat and prevent the planet from freezing out, giving rise to even liquid water on the surface. Sea floor volcanism (very keeping with our Doom) would also sustain life. A rogue planet is also capable of retaining a moon.
However, we get stuck at the point where there is a sun. It would take some heavy refraction by the hydrogenated atmosphere to magnify the size of the galaxy’s center to that of the size of the sun. Besides, there isn’t even a sun at the center of our galaxy, and the radiation emitted by a black hole can definitely not be confused for the warmth from the sun.
A good explanation would probably consist of all of the above, in my opinion. However, it’s highly unlikely. The seasons seem to have definitely caused by the Ice magic brought about by the Others. We have no option but to resort to our simplest argument at the moment – magic.
Special thanks to Dr. Alan Duffy (http://www.alanrduffy.com/).
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