There are several c.g.'s in Kentucky and Tennessee open all year. Over the years we have traveled south in the winter at least 12 times and have never spent a night in a motel and we leave from near Toronto. We always stay in campgrounds and usually dewinterize the second night in Kentucky.
Do a google search and indicate campgrounds open all year. Then call the c.g. and confirm their facilities and price. We have run across KOA's that want to charge $45 a night in winter for just an electric hookup. No way will we stay at a place like that.
If you are a member of Passport America check the parks along your route. There are a couple that might work for you.