I go the opposite way in the winter. Everything is closed camping wise in regard to public campgrounds from Iowa or Missouri on up so we boondock camp at Cabelas, Walmart or Cracker Barrel. Most private campgrounds are closed too. Last year we did camp in a state park in Oklahoma that was open but there was no water and the toilet rooms were locked up. It was below freezing there. The plains states can be brutal in the winter so my advice is to head directly east and then take I-35 north. You will have the protection of the frequent rest stops.