I don't know how wide you can go, but my son is currently tooling around on a 16-inch bike that has two and a quart inch tires on the back and one and a half on the front, on the same wheels :-). LBS said it was the closest they had and that it would work.
Anyway, I was just going to point out that you might want to consider studded tires instead of or in addition to wider ones. I just got one for the front (I have a hybrid, so on the one hand my tires aren't that skinny, but on the other hand, I am very uncoordinated) and it made a huge difference.