I've shot a few with a 22-250. It works, but not my first choice.
If you use one in Wyoming you have to use 60+ grain bullets, which depending on your rifle, may be problematic. Lots of factory 22-250's have slow twists which makes it tough to stabilize a 60 grain bullet.
You could try shooting some 60's and see what happens, mine doesnt like the 60 grain partition at all. I can get 1.5-1.75 inch groups with them, but no better. I did try them out in Texas one year and killed a bunch of hogs and exotics with them. Worked OK on them, but you rarely get shots much over 150 yards there.
The antelope I've shot with it were in Montana and I used the old style 55 grain nosler solid base bullets. Those shoot really well out my rifle, .3-.5 at 100 for 5-shot groups. They held together pretty well, but I stayed off the shoulders. I think you could find yourself in a goat-rope if you hit one square in the shoulder with most of the thinner jacketed bullets.
I've shot my last antelope with a .22 centerfire. I have rifles more suitable.