There's a list for everything online these days, inclucing the United States of Hot Dogs "Best Hot Dogs From Every State". 

Their pick for the best dog in the Cowboy State is...the Weenie Wrangler?

The Weenie Wrangler is a hot dog cart set in up the parking lot at the Home Depot in Cheyenne. Run by a former chef, they specialize in house-made elk and wild boar sausage.

If you're ever passing through the town of Saratoga, another one of Wyoming's best hot dog stands is Hot Diggidy Dog. There's also a food truck in Casper called Rockin' BurgersNDogs that serves a Mac and Cheese Hot Dog.