Bruinpoint,
nfh and others have given you good sound advice on the whitetail situation in most of Wyoming.
I'll give you another angle to consider...not all whitetails are tied to agricultural lands and private lands.
The Blackhills in Wyoming are an example , most all of Western Montana, and portions of Eastern Montana as well. Even though I've never hunted Idaho, I can say for sure that the panhandle and other areas in Idaho (Kamiah/Clearwater/Selway) areas of Idaho have lots of whitetail not tied to ag. and private.
The whitetails I hunt in Montana never see an agricultural field in their entire lives and never leave public land.
I've hunted the Blackhills in Wyoming and there are solid numbers of whitetail on public land there. They receive a lot of pressure, but I've never had any problem finding bucks there on public lands.
The ag. areas, just like the others have said, the amount of public land is limited and whats there gets hit pretty hard. If you're willing to spend some time though, there are WT on some of the public.
Good luck.