Here's one I have for Arizona, I bet it applies in Wyoming, too:
When you look both ways before crossing a dry wash. (In case any cars, trucks, Jeeps, motorcycles, bears, coyotes, or actual giant walls of water are coming).
The one that literally applied to me, the first time I went there, was: I knew I was in Wyoming when I found myself trying figure out how to take a picture of vast emptiness. I still have that picture, but it didn't really capture it.