If you don't mind skipping the swimming pools and water parks, early January weather should be nice. It will be cold, but remember-in Florida, anything is possible as far as weather goes. Also, you shouldn't have a problem with the afternoon showers that frequent the summer months (or maybe just us...I haven't figured it out yet!).
Alot of people take advantage of the Christmas/New Year holiday to go on a family trip since the kids are out of school, but because most schools are back in by the 4th (or close to it), the crowds seem to start thinning out. You shouldn't have a crowd problem.
Perfect timing, if you ask me!