Like the others have said, everything weather related is tied to your weather seed. There's over 2 billion seeds the game can choose from when you create your island. It will usually snow at least a couple of times in the first couple of weeks of December, before it's actually covering your island. Every single seed has a winter "storm" on December 10th - where it snows just about all day long, with at least a few hours of "blizzard" conditions. This is so that it makes sense when the island is covered starting December 11th. Then you can count on having a LOT of snowy days for the rest of December and January.