So, my first fan theory.. (No idea if this idea has been mentioned before).
I reckon Game of Thrones and Adventure Time are in the same universe, but they happen at different point on the time line.
GoT happens after the Great Mushroom war but before the catalyst comet. GoT is basically how the humans recovered from nuclear war, but that all stops when the catalyst comet hits.
When Simon died in the farm world universe, we learned the Ice Crown when skits and froze the earth. Maybe the stupidly harsh winters in GoT are a result of the Ice Crowns mood swings with previous owners/when it's lost previous owners.
It's a fairly loose theory so I'm gonna work on it some more!
Comments welcome but if you thinks it's a dumb theory don't be a dickhead :)