You can buy whatever property you want wherever you want, but, be aware that, in Wyoming, you will be considered a nonresident for hunting purposes until you are domiciled and have continually resided in Wyoming for 365 consecutive days (90 days for active duty military stationed here). So, there won't be any advantage other than owning an asset unless you actually move here. That means higher license fees, having to draw for just about everything, and lower odds. You also can't hunt in a wilderness area without a guide.
https://wgfd.wyo.gov/Hunting/Am-I-a-Wyoming-Resident:
Can I apply for a Resident License?
To qualify for any resident game and fish license, preference point, permit or tag, a person shall be domiciled and shall physically reside in Wyoming for one (1) full year (365 consecutive days) immediately preceding the date the person applies for or purchases the license, preference point, permit or tag and the person shall not have claimed residency elsewhere for any other purpose (including, but not limited to, voting, payment of income taxes, purchase of resident hunting, fishing or trapping licenses, etc.) during that one (1) year period.
Any active duty member of the armed forces of the United States who has been stationed in Wyoming for ninety (90) days shall qualify for resident licenses so long as the member remains stationed in Wyoming.
I am not familiar with landowner tag rules, and whether they apply to nonresidents, but they require an amount of land that could get expensive, there are a lot of rules, and they are limited to the particular land to which they apply. That is its own research project.
