I've commuted a few times during the winter even with snow on the ground. It's all about the tires. The tires are the one who is in contact with the ground. Get a decent set of knobbies and make sure you're gear is waterproof and you'll be good to go. As for under the helmet, a do-rag is good but on wet days, i've wrapped the top of my head with a plastic bag underneath my helmet. Biking in the snow is pretty fun and it's a real test on your bike handling skills. Good luck!