We have been going to the Gulf Coast for several years from mid November to early January and the weather is nearly always beautiful. The rainy season is past and it can still be very warm. It is nearly always warm enough to eat outside during the day and,although the evenings can be cooler, we are often still sitting by the pool until late evening. Apart from Thanksgiving and Christmas the area is still fairly quiet in comparison with January to April.
We went to Marco Island the week before Christmas two years ago and it was very busy.