We have gone twice in late Jan. We find that the weather is just a bit warmer and comfy.
This year we are going the last two weeks. We still pack lots of warm clothes for the evening. Hats, finger gloves, sweat pants for under kids' pants, jacket.
But you know, really less crowds! The only drawback in Jan is you don't enjoy the water parks as much with the cooler daytime weather. But we aren't there for that: we are there for the rides and stuff.
Have fun!
2000 Dixie Landings
2001 Sheraton Vistana Villages
2003 Marriot Little Lake Brian.