Yeah, I'd take those things into consideration I agree about Utah and Bozeman but Bozeman isn't all of MT. But know that times are changing for Wyoming. A lot of their money comes from the energy sector which is one reason they have lower property tax and no state income tax. With Biden in now and hammering gas and oil they are already proposing an income tax because they have a serious budget problem now. I can't find the article but it shows that though jackson can't grow much, the area surrounding it can and is on the Idaho side especially in Driggs and Victor. This is where the majority of the workers and locals actually live. On the west side of the mountains there is plenty of room to put in developments and it is a lot cheaper. So I would just be aware of that situation. Also, skiing there especially at the Jackson hole resort is like $2400 a person for a season pass. Also, it's hard to get the true data on movement to the Jackson area because a large portion of them are 2nd or 3rd home owners and most are from California. Just look at the voting for the 2020 presidential election. The light blue one is Albany county which is where University of Wyoming is at. I will let you guess the dark blue one.
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And to the OP, someone already mentioned LDS, because the whole star valley is based around a LDS temple.
Anyway, not trying to dissuade or persuade you or anyone way just giving my input and research over the last several years. Just depends on what you want and are willing to pay for it. I'd recommend renting a short term rental in the winter time to see if it is what you want.