I bike year round in Madison, WI except when really heavy snowstorms (cuz I'm terrible at riding in snow). I have a 15 year-old mountain bike that I use for the winter. I actually use studded tires (Nokians) for the winter riding. I don't know about the winter tires mentioned above but Madison does not clean its streets as well as Chicago does (I lived there most of my life) and I think the studs are necessary for me.

So, consider getting an old bike that you won't mind beating up and consider investing in studded tires if you plan on being on icy streets.

Oh yeah, my derailleur is usually useless under 5 degrees or so (frozen).