Even if you are a beginner, you can still surf in the winter. The important thing is to wear the proper protective clothing. If you are on the East Coast, you will probably need a full "dry suit" as well as covering for the head, feet and hands.
If you are on the West Coast, you will need a 4/3 full wetsuit, and then as it gets cooler, optional gloves and booties. (The farther north you are, the more you'll need those gloves and booties.)
Sometimes you'll get what surfers call an "ice cream headache" when you get doused by a particularly chilly wave but you should feel pretty warm in the right clothing. With the proper gear, you should be able to get an hour surf session in no problem.
Since the waves tend to be bigger in the winter, and there are fewer lifeguards out, do be careful.