I agree with the "straight south, then west" advise. You could always find a freeze anywhere along the route, but you might also find it in the 60's most of the way as well. The further south you get, the less likely the chance of freezing.
We also use red pop (anti-freeze) for flushing, and take a few gallons of fresh water for drinking and coffee. The showers in the park are what we use too, but make sure that you check the parks first. Many of them, even down into KY or MO shut off ALL the water to the park for the winter......including the washrooms. We always took I-57 and stayed at the Motel Marion RV Park (I don't know why the "motel" in the name, since there's no motel there, but it's a nice RV park) at exit 53. Full hookups, open all winter, SPOTLESS showers, restrooms, and laundry. Pretty reasonably priced too at about $25. By the time we hit Marion in southern Illinois, the weather was usually warm enough to de-winterize. If still cold, we'd wait till the next night in Arkansas, Louisiana, or east Texas. As you head west through Oklahoma or Texas, watch for snow and ice storms, because that's the area that seems to get hit the worst. Keep a weather radio handy, and use it. They're pretty good about giving you enough warning to find a place to sit down for a day or two until it thaws.