DAMMIT! I always forget about Mamoswine. He just never shows up on my radar. How about a mixed Ice/Ground Type then? And yea, he has common weaknesses, but really look at them. If he's fast enough, no Grass, Fire, or Steel Type is switching in, unless it's a scarfed revenge killer or named Scizor. So, really, all he has to do is worry about Fighting and Water Types, unless he's really fast and has a huge movepool that consists of Psychic and Thunder Punch.
But by how much is what I'm wondering. Will it change drastically like some Pokemon just wont ever appear in winter, or will the rarity change by about 50%? Will Fire Types be more common in Summer and Ice Types in Winter? Will some Pokemon be hibernating in the winter and you can find them sleeping in caves? Those are the important questions.
I like that theory. I may end up changing my birthday, though, so I can start in winter.