We've gone a few times in January/February. Our experience was much like what others have posted.
Weather:
Warm or cool weather. Usually a mix over the course of a week. First trip it was cool/cold and drizzly the entire week, but we still had a lot of fun. For me, best clothing was joggers, tshirt, heavy hoodie, and light cloth gloves/stocking hat. Kept me sufficiently warm without having to wear jeans and a parka on Expedition Everest.
Crowds: slightly more crowded in January, but that is a good trade-off from the humidity grossness of September.
Pool: probably not. When I took my nieces/nephew we did swim in the cold cloudy weather at BLT. We'd go down the slide and then hop over to the hot tub.
Waterparks: I wouldn't waste my time.
Bottom line: If you are a cool weather lover and hate humidity, this is the time for you!