Winter is the dry season in Florida and the humidity drops considerably in the state. Compared to NY winters, you'll find the sub-tropical climate of N. Florida to be quite warm up until mid-December. It'll cool down to temps ranging between a high of 68° and low of 44° on average between Dec. and March and get warmer as you move south into the tropical region. There's always a chance of a cold snap in Florida. Regardless, you're going to see native Floridians in long sleeve shirts, sweaters and jackets during the winter. Acclimated to warmer temps, 55° in Key West is quite cold to natives and implants having lived there for a couple of years.
Georgia, North and South Carolina are doable in the winter. In NC, you want to stay in the Piedmont and Coastal areas where campgrounds are open. You may get a day or two with a little snow or an ice storm that comes through. Still, far better than NY conditions. Generally, CGs in the NC mountainous areas are closed. Good luck in your travels. Travel safe.