Cotton kills. I just picked up a mountain hardwear soft shell on sale at rei. Its so thin it seems like it wouldn't do anything, but its quite warm and stops wind. I didn't buy it for riding in, but they way its cut, it would be fine on the bike.

For michigan winters you will need some insulated pants ("tights" but they aren't all tight), and a good riding jacket. Obviously gloves and head protection and some good socks. Have fun in the snow!