We usually go right before or after Christmas. The crowds are really, really light, and normally the weather is warm during the day and cool in the evenings. This January, however, it was FREEZING!! My DD and her boyfriend stayed out for Illuminations one night and it was about 45; they froze! A good rule of thumb for Florida in December is pack for every season. Take shorts, tshirts, sweatshirts, long pants. Bring a light jacket with you to the park even if it's hot when you leave your room. You'll most likely need it later!
Also, if you're going to Fantasmic, take a beach towel or a blanket to put on the bench! Those suckers get really, really cold.