Good advice here, even though BrentD is right - there aren't actually any deer out west anymore.
If you really want to backpack, go right ahead, but... either camping near your car/truck or just basing your hunt out of a motel or rented cabin/house is pretty sweet. Something about a hot shower at the end of the day, a good breakfast before heading afield....
Wyoming - I believe this is still true - if you want to hunt the wilderness areas, you've got to hire a Wyoming guide.
But there is a huge amount of public land, Forest Service, BLM, etc... That can be hunted without a guide.
I live in Washington and do most of my hunting here, but I "go east" to Wyoming about every other year. Wyoming has been real good to me over the years with elk, pronghorn and mule deer.
Here's an example of how a buddy and I did a hunt, several years ago in Wyoming. We got our nonresident mule deer tags, made reservations at a motel. Check availability, a lot of them close when the tourist season ends in September. Stayed at the motel. We'd obtained permission to hunt a large ranch, and also planned to hunt public land. Turned out that we just weren't seeing many mule deer. Scratched our heads and decided that maybe the deer hadn't migrated down to the lower sagebrush areas we were hunting.
Drove farther up into the mountains and hiked up a canyon - sure enough - mule deer!

My buddy took a big fat 3x3 buck. We were running out of time and I could take a doe, so I did so. Being able to shift our hunting area by 15 miles and go thousands of feet higher paid off. We didn't get the big bucks we sought on that trip, but have done well on other trips since then. We did have to pack our boned out deer about three miles back to the trailhead. No problem, just be prepared for that.
Also - up in that canyon in the high country, we came upon grizzly sow and cub tracks. Never saw the bear, but we were certainly on alert while boning out the deer and packing them out on our backs!
Regards, Guy