We've been in late December, never January, but I'm assuming its about the same. For us, its the best time to go, the weather is perfect! We would leave the hotel in the mornings in shorts, t-shirts, and light jackets. the jackets usually came off by lunch and we were comfortable the entire day. Once the sun started setting we would break out the jackets again. If we were out late enough (we were at the Christmas Party until after midnight) we brought gloves and hats and heavier jackets. Florida is humid, so when it gets cold, its a wet cold- the worst!
I would definitely keep checking the weather as your trip approaches, but I would pack everything just to be safe. Another year we went in March and an unexpected cold snap hit while we were there. Disney ran out of gloves and was selling just generic black ones they probably picked up from wal-mart for $1 for $10 a pair. I was actually desperate enough to buy them- don't make my mistake!