I have been in Jan/early Feb a couple of times and will be doing the land/sea Jan. 19-26, 2006. The weather is anyone's guess. I've been there with turtlenecks, coat, & Mickey hat, but I get cold easily. However, 2 years ago there were record highs in the upper 70s/low 80s every day!
Crowds - there are none! The week after New Year up until President's Weekend is one of the emptiest times to go. I would definitely recommend it, unless you are set for water parks, lounging at the beach, etc.