Yes, you
will need to winterize, and probably before you get to central Oregon.
Weather is a definite concern that time of year, especially in Wyoming, Nebraska, Iowa & Minnesota. If you can take your time, you may be able to get there in time for closing on the new house with a minimum of stress, and some extra days for layovers in case of bad weather. Not just snow but ice (sometimes black ice, which is dangerous because you don't see it until you're on it) and wind are your enemies during the cold months on the plains.
80 is out of your way but more likely than 90 to have a bit warmer temperatures, perhaps. Along I-80, just checking KOAs, there are a few that are open in late November, noting that they offer "limited services" during the winter months: West Omaha NE, Cheyenne WY, Rock Springs WY, & Laramie WY. Others that might lie along your route(s) that are open all year: Boise/Meridian and Pocatello ID, Redmond OR, Waterloo IA, Sioux City North (SD), and one that might be near where you are moving to, Hixton-Alma Center WI. That's just KOAs; there may very well be other private campgrounds open as well, though the majority will not. State parks will most likely be closed all along the way.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375