I live far enough south so that I don't snowbird all season, will just go somewhere warmer for a month or two (January and February). So I leave sometime after the New Year, and am usually home before the end of February, because I might have to be doing Spring cleanup on my properties that early.
Sometimes I take the RV to Texas Hill Country, the southern Texas coastal plain or the Texas Gulf Coast, but my snowbirding isn't always by RV. I might take a long tropical cruise, or fly to a warmer destination. RV snowbirds are just a fraction of the people around the world who migrate with the seasons, most do it sticks and bricks. I also go to the Mississippi Gulf Coast, but not yet with the RV, since I when I was going I had a daughter there to stay with (same for San Antonio).
My cousin snowbirds by RV. His summer home is in the northern Lower Peninsula of Michigan, more comparable to Wisconsin. He leaves for Florida at the beginning of October, takes a couple of weeks to a month to drive down, stopping in places like Destin or the Nature Coast along the way. His destination is Fort Myers, same RV park year after year, to connect with the same group of motorcyclists who spend the winter riding around South Florida. He doesn't come back north until May or June. I don't know how many other places he has tried, as he has lived and worked in Florida, Southern California and the desert Southwest. It is the personal connections that take him to Florida.
NE Oklahoma, NW Arkansas, SW Missouri is also RV snowbird country. We start getting a lot of people from the northern plains (the Prairie provinces and northern tier states like the Dakotas and Minnesota) in September, when it is still as warm here as it was in Summer where they come from.
Many stay here through October, some into early November, then move down into East Texas, southern Arkansas, northern Louisiana, and the Texas hill country, waiting until the Gulf Coast or the Rio Grande Valley cools off before moving further south. So RV snowbirding doesn't need to be one big move, you can move gradually and stay in places where the climate is what you like. That's a big advantage over the S&B snowbird who has a house in Connecticut and one in Palm Springs, or a home in Green Bay and the other in Naples. They have to choose between staying until it gets too cold or going while it is still too hot at the other place.
So if you start moving early, a good place to stop along the way is Grand Lake O' the Cherokees in NE Oklahoma. We like the community around Grove, on the east side of the reservoir, and usually go to Cedar Oaks for October and November "campouts" but there are other decent RV parks too, and at least three state parks on this reservoir.
Then maybe down to Pat Mayes Lake, Lake Texoma, or one of the other reservoirs in north central Texas. After that, if still headed toward the Rio Grande Valley, go to San Antonio (RV park we use is Traveler's World but there are more resort-like places over by Sea World) or Fredericksburg. If headed toward the Texas Gulf Coast, next stop after northern Texas could be the Houston area (if you are into big cities), Galveston for the closing of the season at the beach, or on down to Port Aransas/Rockport area which is for some their ultimate winter destination rather than the RGV.
If going to the Mississippi Gulf Coast, enroute stops could include the reservoirs in NW Arkansas (around Rogers), the Ozarks, or on the Arkansas River around Russellville to Conway. When time to move on from that, there are some nice RV parks in Arkansas Delta Country. During planting and harvest seasons these are there for seasonal workers, but after the workers leave the same parks become snowbird resorts. A particular area I'm thinking about is around Lake Village, just west of the crossing into Greenville, Mississippi. Then the next move, Greenville to Gulfport/Biloxi or on over to Gulf Shores in Alabama, is less than a day of driving.
I think I've given the idea. I can't help with details down through Illinois, Iowa, Kansas or Missouri because I am starting more to the south. Maybe about a day's driving north of Grand Lake or the Rogers Arkansas area, I would choose to stay for a while at Lake of the Ozarks, or in the Hannibal area, maybe also Mark Twain Lake. But no later than late September, early October that far north.
A final thought on this migration. Most of the people who come through this part of the country are seniors, and have the senior pass for Federal recreational properties. They stay at Corps of Engineers recreational access facilities for $8 to $10 a night with their senior discounts. Two weeks at each facility, then move on. You can do this all through the valleys and tributary areas for the Mississippi, Missouri, and Arkansas rivers, where a huge network of flood control reservoirs are managed to keep the Mississippi navigable. The places are not fancy, don't have camp stores (you'll need to go into a town to shop) and do have seasons. But as you go more to the south, the seasons are longer. You just have to do your homework to time your gradual migration to use the head and tail ends of the season. E.G. where I am, most of the Corps campgrounds open April 1st and close the last weekend of October. This is because the volunteer work-campers who staff these parks are also snowbirds and want to be moving with the climate too.