So close and yet so far....
Wyoming has tons of public land, BLM, State, National Forest. You can hunt Deer (white tail or mulie), elk, antelope, moose, coyotes, prarie dogs, and with a lot of luck at the draw, sheep.
Population density is the lowest in the country. Where I live there are 750 people, it's 12 miles to another 200, 20 miles a different direction to 320 more and 45 miles to the nearest "real" town. 80 miles to Walmart.
I paid 55k for 4 bedroom, 3 bath, 2 1/2 car garage although prices are going up lately.
Then there's the weather. Right now it's a balmy 54 degrees with a day time high of 62 anticipated. It should warm up to 80 later this week though. Shooting long range is an early morning pass time. By mid day the wind gusts can exceed 30 mph virtually any time of year which makes those -10 January days rugged to say the least. Most of us hunker down from December - May and dream of spring time. There's a nearby town named Saratoga that may be worth looking into for you. Housing prices aren't bad and it seems to be in a valley that shelters it from much of the wind, although low temps are low temps. You can look on Weather.com for annual average temps, highs and lows. Lander is pretty temperate (but not as cheap) with more in-town shopping and it's at the base of a major mountain range. Casper and the afor mentioned shoots are about 2 hours from me, 3 hours from Saratoga and 5 from Lander. I think it may be faster to go to Salt Lake for long range shoots from Lander.
Hope this helps.
Coyoter
I should have added that General Elk and deer tags are available over the counter to residents and available if you don't draw in a limited quota area. Antelope are virtually all limited quota (draw) tags, but early after the draw there are many leftover tags that can then be purchased over the counter by residents.