Wyoming has been great for me and my family, we moved to Cheyenne several years ago and we like here so much that I think I'm going to pass on a job opportunity in Montana and just plant roots here in Wyo. The winters are long, but like others have mentioned, look at the recreational aspect of all seasons. Since winter is the longest season here I'll lay it out from my experience from there:
Winter: Ice fishing in dozens of lakes for any species you want, skiing near or far in some of the best in the country, cross county skiing, busting out the snow machines, and ice rinks for the kids.
Spring: Bear season (baiting is legal here), turkey season, everything is defrosting so no need to water the lawn.
Summer: Fishing is great to include miracle mile, the reef and so on, trap league is amazing and every Wednesday night here, water sports (skiing, boating, swimming, wake boarding, not to mention Glendo has a huge sandy beach for the kids), hikes, Yellowstone, the tetons, camping, riding the sand dunes in Colorado just across the border, and so on.
Fall: Screaming elk, rutting antelope, mule deer, whitetails, upland birds, migratory birds and more.
Public land is plentiful, there is so much to do here it's a shame that the days aren't longer and gas wasn't cheaper. There's also jobs and some really good ones besides Jackson, Jackson is nice, but inflated on all accounts. I don't recall who said it on a recent podcast, but it stuck with me and it's a game changer of a quote, "I truly believe that the outdoors in Wyoming is what kept my family together." For a guy who left the nest at a young age seeking adventure via the military, I've found where I need to be and found a place that gives me the best chance to lead the life I want and to keep my family intact with the things we love to do. Cheyenne wasn't my first choice in Wyo, but it's worked out to be the best. Proximity to everything is nice. But anyways, good luck and I hope you find what you're looking for.