I'm not from TTUHSC, but I'm from near the area. Texans are notoriously friendly and outgoing. Don't be shy about asking questions! Lifestyle is laid back- everything's "bigger" in Texas, as they say, but expect the pace of life to be a little slower compared to "big city" life.
While Texas is an entity of its own, it does have a lot of similarities to the South- good manners will get you far, especially with the hospital staff! Yes ma'ams and no sirs will get you far! For the most part, expect a friendly patient base, too. People are outgoing and warm, and you'll do well to create an atmosphere of friendship moreso than a paternalistic Dr./patient relationship. Don't just ask about their medical problem- take the extra minute to greet family members or "personal" questions (e.g. If you see them wearing a Dallas Cowboys jersey, look them dead in the eye and say "WHO DAT!" 😛 Just kidding, but in all seriousness, ask if they're a football fan.)
Weather will run the gamut while you're there. Pack layers. September and October can still be oppressively hot (in the 90s) but late December can start getting chilly. That being said, prepare for temperature swings in December. It may be in the low 40s when you get dressed that morning but could well warm up to the 60s that afternoon, making that sweater you put on a bad idea.
Take time to check out the culture. Eat barbeque, try out the local chili, browse a Western wear shop, see a rodeo, above all, remember to have fun!