hi bob and also hi, josie. we have stayed in SC many times, love it, love it, love it. as to camping, we tend to head toward the beaches. our two favourite spots (we stay away from private campgrounds if at all possible) are myrtle beach state park and hunting island state park. the weather won't be hot in jan/feb/march, though. i do not know what temps you are seeking but check out with the weather network for some average temps so you don't go and are disappointed.
georgia is also very nice and we have some favourites there, too, but again, temps will be cooler than you may wish. but isn't the planning/hoping/dreaming stage so much fun?!
we have spent, on average, 8-9 weeks per winter in our 13' and are both still alive to talk about it.
you downsizing for the winter from 31' to your 13' for that extended period (irrespective of your "breaks" when you head home) will be a good test of your decision!
one thing for sure, it'll be a great time. the atlantic coast has much to offer.