a couple of years ago I did a drive to Santa Fe, New Mexico, which is about 1/2 way between SLC and San Antonio. Its a beautiful drive, but its a lot of winding, two lane roads through Colorado and New Mexico. Taos and Santa Fe are very nice, but Albuquerque is sketchy.
Roughly 21 hours from wasatch front. Albucrackmeth is about halfway. Santa fe, is nice if you like art. Mesa Verde is a little side trip might be neat to see with some snow. Fly fishers can fish the San Juan. And iirc White Sands National Monument may be a not too far from the main road diversion.