Once you get to central KY, most campgrounds will be open, some may have limited facilities, depending on the weather.
We like
KOA.com and they are well spaced all along I-75 right into FL.
We generally spend the first night at the KOA in Corbin KY, 2nd night at Chattanooga South. We time leaving here to get through Atlanta after 10 am. There is another KOA at Macon Ga, if you have made better time from KY. All of these are within 1/2 mile or less from the highway.
If you don't care for the KOAs, there are many other choices very close to I-75.
Last Feb, we only got the Bluffton (central OH) the first night. The KOA was open?, electric only, and semi plowed sites, had to wade through 2 feet of snow to plug in. NO restrooms, showers, water or dump available. The electric was definitely needed in the -29F weather.
Ken