I do it every year (of course, I live in Ga, USA, so the winters aren't that bad here, as a rule), so I am going to say, yes, it's very doable. I am sure most IDIDABIKE riders will agree with me.
Use a commuter, or mountain bike with some good knobbies. The smaller frames are a bit more maneuverable than road and fitness frames, and this helps when you are trying to avoid ice patches. Dress warm and breathable, and be prepared to go down a few times from unseen ice patches. The warm layered clothing is good padding when you hit the ground....... Winter riding is one of the few times I will wear a helmet.
Riding in the winter is a great adventure, if you maintain the right attitude about it. It's not just a ride...it's an adventure.Think of it as emulating the great explorers, like Roald Amundsen, Robert Perry, and Richard Byrd.......