Yup.. rode my 20 year old Huffy MTB this winter, and it did great. I'm going to keep an eye out at garage sales for a spare or two, as it looks like my drivetrain will probably only last a few seasons. It's cheaper to buy a new bike at $20 from a garage sale than replace components, and I don't have to clean the drivetrain every day.
I'm not even sure cleaning the drivetrain every day would be enough. Besides, it would get expensive as I'd have to use petroleum based products to clean it since the water would freeze and cause all other kinds of issues.