It's a few years back, and may have changed, but the last time I hunted Wyoming one could hunt coyotes without a license. Discussion with the agent in that area indicated there could be a problem with perception.
Meaning after I tagged out I could scout neighboring units, and hunt coyotes. However, packing a .338 RUM, could be interpreted differently than if I had a .22-250.
Other times of the year it might be interpreted differently.
So the answer is a qualified yes. At the very least make a call pre-trip, and feel the locals out, and give advance notice.
