Depends on how much of a hurry you are in. The fastest and most direct route is I-35 to San Antonio, then I-37/US-281 to Edinburg-Pharr-McAllen area.
If you are enjoying a leisurely migration, then I-44 out of Oklahoma City to Wichita Falls, then US-281 south to San Antonio. My daughter's family got transferred to the air base in Wichita Falls about the time we retired and started RVing, so this became our snowbirding route. It avoids the heavy traffic on I-35, not just Dallas-Ft Worth, but also the traffic problems of Austin, Waco, and the suburban sprawl around San Antonio, which along I-35 extends to New Braunfels.
Starting at Wichita Falls, there are a number of good communities for enroute stays in Hill Country: Lampasas, Johnson City, Mineral Wells, with several state parks along the route. Most of the route is two-lane with "passing" shoulders, and in the rural sections higher speed limits than you probably want to use. The towns will slow you down.
It comes back to how much of a hurry. We can drive San Antonio to Tulsa in a single long day, using I-35 to OKC, I-44 to Tulsa. We did this for many years, to have Spring Break vacations in SA. Using 281, I've never gotten to San Antonio in less than a day and a half. Can't measure this for the RV because we always did a lot of sightseeing on the way to San Antonio, and on to the Gulf Coast.
A good first stop, but more than five hours out of KC, would be Twin Fountains in Oklahoma City, right after the I-44/I-35 split, by the exit for Remington Park race track. I'm not sure what you might find open in winter further north. Probably Cedar Valley just west of Guthrie, some folks snowbird there. I've driven KC to Wichita a few times, I've not noticed any camping facilties or used them. An OKC stop sets you up for stops at Wichita Falls, then somewhere north of San Antonio (visiting that for a few days can be nice). From SA you should be able to reach your destination in a driving day.
I can't vouch for US-281 breaking off south from I-37, as I've always used US-77. I expect 281 would be pretty desolate, if by that you mean there is not much between the towns, which tend to be 30 minutes to an hour apart. That's Texas, some big areas of empty separating the river valleys, along which the towns and cities string out; no water, no settlement.
For a really slow trip, come down US-69 from the KC west side, or US-71/I-49 from the east side, down to I-44, then get off at Afton (US-59/60) to stay at one of the several RV parks around the north end of Grand Lake. We like Cedar Oaks on the east side on US-59 just north of Grove, but there are several other year-round "resort" RV parks in the area, and the state park campground at Bernice stays open all winter unless the water is high.
But this would not be for a January departure, we start getting winter in January. Grand Lake snowbirds are usually there in late October to late November, for a stop-over enroute to their next stop in Texas Hill Country or San Antonio, where they either winter or stay for a while before moving on the the RGV or Corpus Christi.
