As you travel south you will find most parks open with full services.
Last year in February we traveled north,
, to Elkhart, IN.
We found campgrounds open, but had their water shut off.
So, start with fresh water in your tank.
Traveling I-40 we have stayed at these:
Parkers Crossroads, TN - Parkers Crossroads RV Park
Memphis, TN - Agricenter International RV Park
Hazen, AR - Lower White River RV Park
For me, I would try to schedule my travels to NOT stop in Memphis.
It has too many people!
Hope this helps,