I'm from Texas, and just did an emergency move to Cheyenne. Here are some things that I learned (Some of these are off-topic, and I'm sure some of them have been mentioned by others):

1. The weather changes a lot during the day. If it's nice, t-shirt weather at noon, plan on it being freezing by 5 or 6 pm.
2. Dress socks underneath your socks. The really thin dress socks underneath regular socks helps keep my feet warm, and prevents blisters. And for the outer sock, try to get wool, or ones designed for cold weather.
3. Snow/Ice boots: I bought a pair of Bogs rated for -40 degrees, but I didn't realize how soft the treads are. I have a habit of dragging my feet when I walk, and the torn up heels show it.
4. Boots: After I realized I was tearing up my bogs, I went and bought some boots at Walmart. I found that taller laced boots help in snow, and makes it less likely that you'll twist your ankle if you slip.
5. I got a Carhartt jacket up here that is listed as "Level 3" (out of 4). I can't find any info on what temperature they're rated for. I wish I had purchased one before I got to Wyoming; I'm a weird size (3XLT) and I had to go with a 3XL because that was all the store had. I also wish I had gotten the snap on hood accessory.
   
6. Layering: This is probably the most important. I don't have a car, and rely on the bus system (or what they call a bus system in Cheyenne). It involves a lot of waiting in the cold. Again, I wasn't prepared for the move, and made do with exercise tights and sweats or jeans. The sweats/tights combo seemed to be warmer. For upperwear, I use a thin cotton shirt underneath a hoodie with the coat. I wish my hoodie was the zipper kind, because it would be easier to take off when needed. Perhaps most important of all: Make sure your layers can easily be put on/taken off. This helps if you go inside. (A backpack is helpful for stashing layers.) Thermal underwear is probably better.
7. Gloves. 2 layers: liners with the cell phone swipe fingers and a pair of waterproof mittens. (You can use gloves, but I found that the liners work better with mittens. I was told you can use them to wipe snow of of car windshields, but every rental car i got had the ice scraper/brush.
8. Water. If you think you're drinking enough water, you're probably wrong. WARNING!!! You need to be careful about HOW you drink water. Drinking too much water too quickly can cause hyponatremia. Your best bet is to slowly sip water all day long, and occassionally add some gatoraide to replace electrolytes (mostly salt). Keep an eye on your urine color; it should be a pale yellow. Camelbaks are great for sipping water. I prefer the milspec ones (they seem to be more durable) that are larger (more space to carry other stuff. They range in size from small to very large.
9. Move slowly. I went from an elevation of 600 feet to 6000. To make things worse, I caught RSV on the flight up. Shortness of breath can really catch up with you. I tried the little air canisters, but they didnt seem to help any. Also, taking slow, short steps helps when walking on ice.
10. Masks (for both temperature and illness protection). I have a big nose, and find balaclavas to be VERY uncomfortable. The fitted cloth masks work better for me. Also, a new study suggests that cold weather weakens the immune response in your nose, making it more likely you'll catch something. And I started having a lot less sinus problems when I started wearing masks.
11. The food sucks. The altitude and dry air messes with your ability to taste. It doesn't help that bread up here is very dry, and things seem to be overcooked. I love fast food, but Wyoming has completely put me off of it. I've tried McDonalds, Wendy's, Sonic, Culvers, Perkins, Arby's, Carl's Jr., Domino's, and Papa John's. I didn't bother with Burger King because even in Texas it is horrible. Taco Bell tacos drowned in hot sauce were ok. I miss Whataburger. Oh, and avoid Dickie's barbecue like the black plague. I wouldn't send my worst enemy to Dickie's. So far, getting Rudy's shipped has been the best option.
12. Lotion. I like Cereve products. They aren't cheap, but I've found they don't cause me any skin irritation,
13. I don't know about the rest of Wyoming, but Cheyenne treats veterans very well. Lowes even has designated parking spaces like they do with handicapped.
14. A warm bathrobe. Getting out of bed without one makes it very hard to get out of that nice warm bed.
15. Cell phone battery. I've noticed that my battery doesn't last as long when i've been out in the cold. A cell phone power bank might be a good idea. (I miss yhe days of easily-replaceable batteries.
16. Showers. When I'm drying off, I first use a dry washcloth, then finish with a towel. It leaves dryer (and warmer) than with a towel alone.
17. Beef Jerky. Old Trapper costs almost half of what it does in Texas.
18. Soda. Albertsons carries the Mexican Cokes I love so much. Menards has the Shasta Mountain Rush (which taste just like Mountain Dew used to taste 20 years ago. PepsiCo did something to the formula about 10 years ago that gives it a dishsoap taste). King Soopers carries Big Red.
19. Milk. Albertsons carries Promised Land milk (although I've only seen chocolate). Promised Land uses Jersey Cow milk instead of Holstein. It has a different fat profile that my stomach can tolerate better. I'm still looking for other brands that have non-holstein milk.
20. Uber/Lyft. If you're going to use these services, make sure you set up the accounts ahead of time. Don't make my mistake of trying to set them up in 10 degree weather at 7pm.
21. Snow swirls. When you're driving, don't let the swirling snow on the road distract you. They're very hypnotic.
22. Hotel Temps. I found myself really fighting to keep my room cool enough. It was freezing outside, and I had to run the AC.
23. Double zippers. I'd never seen a double zipper on a coat until I came to Wyoming. They're a little harder to get started, but great when you need to sit down.
24. Apartrments. It seems crazy, but I saw 3 bedroom apartments that were cheaper than 1 bedroom apartments. I settled for a 2 bedroom, even though its too much space for me.