As others have said, there is no Congressionally designated or "capital W" wilderness on BLM lands in Wyoming, which is a real shame. I haven't been to all or even most of the WSA's in the state (I think there's 45 or so), but the one's I have been to in the Red Desert and in SE Wyoming are pretty solid spots for people who are willing to work for it. Some of the WSA's in the Red Desert are tens of thousands of acres in size, and rarely visited by anyone. If I'm ever lucky enough to draw a 100 elk tag, I dream of hunting elk in the steep canyons of the Honeycomb Buttes as they drop off of Continental Peak and turn into a maze of hoodoo's and multi colored sediments. You could go for days and hunt elk that are largely left alone for the fact that there are a ton of other places in 100 where you could kill a solid 300 plus that would be a much easier pack out. I don't even feel bad throwing that out on the internet, if someone is lucky enough to draw that tag and has what it takes to hunt that country, I hope they do, and I hope they enjoy the hell out of it and want to advocate to keep it just how it is, Wild!
On the topic of WSA's in Wyoming I haven't heard much about the Wyoming Public Lands Initiative for a while. That whole process can largely go to hell (in my not so humble opinion), and the WSA's can stay exactly how they are, at the very least, until we have more folks that are friendly to wilderness in the political arena. It was always my strong opinion that WPLI was a process that was meant to do one thing, and that's release a significant number of WSA's in Wyoming. I'm sure that some of the County Comissioners involved had good intentions in regards to generating public involvement and possibly getting some WSA's recommended for designation, but I don't think that really why the WPLI was started and I can't imagine that those recommendations would have ever gotten the same level of care at the legislative level as the recommendations for release. Which, to come full circle, is a shame. We have a lot of acres of WSA's not just in Wyoming, but throughout the West. Imagine the potential for additional wilderness protection if Congress were to act to start designating some of these WSA's in the way that Congress designated wilderness on Forest Service lands in the 80's. One can also imagine what would happen if a mass of these WSA's were to be released. I know there would be a lot of happy people that would want to put roads into those area's so they would be more accessible to motorized travel, but to those that love to hunt and recreate in vast open places where people can't drive, the landscape becomes just like the vast majority of all the other lands, a mess of roads, sometimes balanced in their impact but oftentimes at densities that seem ridiculous to me.
What WSA's on BLM tend to lack is the picturesque mountain landscapes that dominate many of our other Congressionally designated wilderness lands. In some ways I can understand how those landscapes were an easier sell for Wilderness designation. But what many of the BLM WSA's, or even "Lands with Wilderness Characteristics" are so damn important for is in their value as wildlife habitat, and as prime places to hunt. A lot of the Congressionally designated wilderness lands in Wyoming are summer or transitional range, and a lot of the WSA's are more in the winter range category. Despite the fact that Congress has slowed way down on Wilderness designations in the past few decades, I am hopeful that in time we will eventually begin to protect more of the BLM areas that are beneficial to wildlife and to backcountry hunters across the West. Once a place is developed, you can't really bring it back. And they're not making any more of the stuff.