I just turned 80 and have been towing our trailer from Michigan to mid Florida or to Texas and back for the past 15 years. If you go to Florida and want fairly warm weather most of the winter try to stay South of a line from Tampa on the West to Orlando on the East. There will be an occasional chilly day or two but mostly mid 70's to low 80's from January to early April. Usually not too many bugs during that time either.
There are hundreds of parks to choose from and all styles of accommodations. Mostly the people are friendly but the coast areas are quite crowded with the snowbirds during those months. If you don't want busy areas, stick to the central parts of the state and areas like Sebring or nearby towns.
Texas is nice also. Very friendly but not as warm as Florida. Lots of history and fun things to see and do there. We have stayed in the San Antonio area and the hill country. The hill country is quite cool early in the winter but warms up nicely in late Feb and early March.
Good luck in your decision. I certainly recommend giving it a try. Sure beats shoveling snow and driving around on snow and ice.
Barney