I've flown down three times, each time we had to arrive at 2:00am!
All I can say is wear LAYERS. It may be freezing cold or chilly when you board the plane but once your in Florida it's warm. Also, when you're on the plane the temperature can vary from Cold to Warm. I suggest everyone in your party wear a tee shirt and a pair of pants. Then, on top of that you can add sweater, coats, vests. whatever is needed.
**Note if you take of any layers while in the airport or on the plane make sure you don't leave them behind!**
Now knowing the temperature of wherever you live, I can only give you tips assuming it will be cold. I live in Scarborough (Ontario, Canada) so each time we go down in January it's snowing