The key to enjoying winter surfing at the Rockaways is all in what you wear and what you should wear is a good wetsuit. We wore a 5/4/3 mm suit that fit like a glove which is also key. Loose suits will keep you from getting warm and suits that are too tight will restrict your movement and make paddling out against the waves harder than it already is.
Our wetsuit had an attached hood and we also had booties and gloves (the same fitting principles apply to those as well). While it’s been a balmy winter so far, we were sure we’d feel some sort of shock from the cold when we eventually ran into the waves. But we did not! This meant we could focus on getting ourselves back on our board and out past the breaking waves where we could rest a bit before trying to catch a wave again.