Wyoming has several species that are legal to take year round. You have to have at least a 40lb bow for small stuff and a 50lb for big game.
Badgers ... need a furbearer license but legal year around.
coyotes ....
jackrabbits .... Wyoming has a lot of the white tail jacks which are VERY large, almost as big as a small white tail deer. And are very good to eat, the best tasting game animal IMO although cottontails are more likely for dinner fair. The jacks are good when young, but the bigger ones I've eaten by frying everything and then giving the hams to my russian wolfhound cross lol. Rabbit gravy is splendid ....
raccoons, skunks, porcupines, red foxes are also huntable year round it seems and are classified as predators along with coyotes and jackrabbits for some reason.
They do change this stuff a lot and seem to bury this info deeply in their rules ... always check first ....