I go from just north of Tulsa to Lansing or the Detroit area, about 17-19 hours moving, to cover a little under or over 1000 miles. If I do it with one stop, that stop is usually around Springfield, Illinois. As a RV trip, I've used the Springfield KOA, but I don't know if that one is open year round.
You are going enough additional distance that the halfway point will probably be closer to St Louis if you use I-44, Hannibal take a more northern route.
I've done this as a RV trip several times in summer, usually two and a half days, because getting camped in the evening and getting away in the morning cuts into the driving day, and we need more fuel stops with the RV, more rest stops with the grandkids. Typical stops going out have been Hannibal (Mark Twain Cave CG, though we did Injun Joe's once) and someplace in west central Indiana. Other direction, with an early start we can reach Hannibal from Lansing, and from there either stop in southwest Missouri, or make it a really long day to come on home. We've also routed through Des Moines, stopping first night in north central Illinois (think it was around the I-39 junction) then again in Des Moines for a day of visiting there. Des Moines to Tulsa is then a long single day drive, you would need a stop if headed to Fort Worth.
Places to stop might be tricky. Most of the RV parks north of I-40 that I've used in spring, summer or early fall are places that close for the winter. I lot of campgrounds in public parks also close, where they are dependent on volunteer staffing, and the volunteers go south for the winter. You might be using parking lots and truck stops.
I'll admit to not taking my motorhome north to Michigan in the winter season. 30+ years of driving to Michigan and back for the holiday season have taught me that wintry roads are a high probability, usually with freezing rain and sleet through southern and central Illinois, southern Missouri, and northeast Oklahoma. Snow is more often probable through southern Michigan, northern Indiana, northern Illinois, northern Missouri, Kansas and. This is a drive I prefer to make in a front-wheel-drive car rather than a seven ton rear-drive vehicle that blows around in the wind.
I can suggest a route to Fort Worth: I-69 to I-94 to I-80, then either I-57 and I-72, or I-55 to Springfield, Illinois, then I-72 west through Hannibal, becoming US-36, then south on I-35 from Cameron to Fort Worth. This route is mostly level, staying atop the Ozark Plateau rather than cutting through the valleys, and is far enough north and on the plains so that the expression of winter weather is more often snow, rather than freezing rain.
Most routing programs are probably going to put you on I-55 to St Louis, I-44 to OKC, to I-35 into Fort Worth. I-55 south of Springfield, and I-44 through Missouri are the sections where I have encountered most of my winter weather delays, maybe something about how the topography of the Ozarks interacts with weather.
I've used alternatives to get around weather and road construction problems. I've gone as far north on I-35 as I-80, and I've used I-44 to St Louis then I-70 to Indianapolis to catch I-69. I've also stayed further south (US-60) to go through western Kentucky, before going north on I-65 and I-69 from Louisville, to be south and east of a weather problem. When going to Detroit I've stayed south of the Ohio river until catching I-75 at Cincinnati, for the same reason, going around bad weather.
Because I might have to make last minute routing decisions, or make changes on the way, depending on the location of a winter storm system, I don't make overnight stop reservations. Winter weather means I don't really know how many days it is actually going to take, or where I'll be when I have to stop for the night or to wait for a storm to blow through so that the roads can again be cleared.
Once you get into the southern middle of the country, you'll find winter weather handled differently than in Michigan. You won't see plows and salt trucks out at the beginning of a storm running in traffic. More often we wait to see if the roads are going to be too slick or get buried, and if they do get dangerous, we close them to traffic. Then we decide whether to try to clean it up, or wait for it to melt. The highways will usually be reopened as one lane is plowed in each direction, and the stopped cars and trucks are towed off the roadway. We might not have multiple lanes cleared for a couple more days, we just don't have the equipment to do the job, considering we get an average of 2-3 snowfalls, and about as many ice storms, each winter.
