Finding something open that time of year would probably be where I would start looking. RV's don't do cold well and even if you do find a campground open it doesn't always mean the water will be turned on. I just wintered in Virginia Beach and the park turned the water off several times whenever the temps got down to 32. As others have stated I would probably go very south and try to find something closer to the east coast or south coast.
Personally I would not want the better half of my very rare two weeks off to be spent mostly driving. If you find something Very South, you will want to remember that that will also be prime snowbird season so you may want to consider reservations for area's south of I-10.
Hope you find something good though cause that first good trip is what sold my wife on wanting to do more camping, and now we are full timing.
If you do stay in cold area's be sure to search this site for winter tips like space heaters and heated hoses, and know you will probably need to refill your propane at least once.