There are 2 US Post Offices in Washakie County serving a total of 8,598 residents equating to 4,299 residents per post office. It's estimated that approximately 13,723 packages are handled across the 2 county post offices annually. Washakie County is a county located in the U.S. state of Wyoming. As of the 2010 census, the population was 8,533. Its county seat is Worland.