Welcome to the forum. Many snow birds make their winter reservations a year in advance. Compared to the frozen north, any place in Florida is a good alternative in my opinion. The further south you go, the least likely you'll see any freezing temps. South of Orlando for instance. Cold snaps are usually brief and daytime temps are generally comfortable in the winter months. So the issue is finding a vacancy.
There are always cancellations, so work the phones. Florida has lots of commercial campgrounds and some very nice military campgrounds. For instance, Naval Station Mayport has two campgrounds, one of which is for stays of up to six months. My guess is they'd be fully booked but it's worth checking. South Florida campgrounds, if you could find a long term stay, could easily be $2K plus per month in the nicer campgrounds. Some decent places can be found for half that.
Some folks just drive down without reservations and manage to spend the winter finding short stays here and there and moving around. We're spoiled and faint of heart. I don't think that would work for us. Good luck. Bob
