People ride all sorts of different bikes in the winter. Your choice largely depends on the amount of money you have to spend. I ride a Trek 4300 mountain bike in the winter. It's fairly entry level and works fine. Your biggest expense should be on proper clothing and studded tires. A decent bike is required in my opinion as well.
After all, I don't ride a Walmart bike in the other seasons, so why would i want to sit on one for 4 months? But that is just me, again it depends on your $ situation and how you see things.