We have been to Florida over Christmas and it was FANTASTIC. We did it just the two of us but have been also with ds when he was 11 mths and also great. Vest & shorts during the day with a jumper in the evening.
Have also done Florida Keys (not for kids, nothing to do) and the Gulf Coast, these are both fab. Have stayed from budget motel to posh 5* hotel and a villa.
With children I would recommend a villa everytime. Eating out there is easy as children are a priority and as their resturants open most of the time you can eat when your children need to. Also 'posh' like Hard Rock Cafe, Planet Hollywood, Garfunklesn and many others.
Shopping, Disney, beaches all great and the weather tops it all.
Have been in Oct, Nov, Dec & Jan. Jan had a bit of frost but this was freak weather to them.
I am so jealous, but with twins on the way we won't be going back again for a while .