Wyoming is a great place, with lots of outdoor activities besides hunting, and our unemployment rate is low. That being said, the job growth is in the oil patch, and if you aren't a young buck that enjoys getting tired and dirty, making a living can be tough. We are in the Boom phase now, but the Bust inevitably comes, and with that, tough economic times. Housing is hard to come by in Boom times, but will be a dime a dozen when the Bust hits. After my police career, I worked with vets on employment issues, and the blue collar workforce is where most people subsist in the Cowboy state. Research carefully before making a move. I saw lots of people who moved to Wy because of the hunting/outdoor stuff, and got very disillusioned after a winter or two. I'm snowbirding in Arizona right now; those winters can get tedious. But then compared to N. Dakota or central Alaska, we don't have much to complain about as far as winter is concerned.
Another consideration; are you a native northeasterner? If so, moving to a place like Wy or Montana is like moving to another country; the lifestyles are very different. Some folks adjust, others are like a fish out of water. If the tables were turned, I can't imagine living in the northeast; I gotta have space! I'm not kidding when I say that some folks freak out in 'big sky' country, where most of our counties are bigger than your state, and the antelope outnumber the humans. If possible, I would suggest that you take an extended trip to whereever you think would be a good place to move, and NOT during hunting season, just to see what life is really like.