I'd do a single speed or possibly a suicide hub fixie. A fixed gear schwinn with very slack angles (and very big lights) was my favorite winter commuter. It gives you a great feel for road conditions through the pedals. Narrow tires work on cleared roads; I have frequently come to a stop and put my foot down, only to have my boot slide away from me.

My only trepidation would be learning to ride a fix with a pooch on the line. In fact, I don't know any good way to run a dog from a bike. How do you do it?