There are 5 US Post Offices in Platte County serving a total of 8,813 residents equating to 1,763 residents per post office. It's estimated that approximately 14,067 packages are handled across the 5 county post offices annually. Platte County is a county located in the U.S. state of Wyoming. As of the 2010 census, the population was 8,667. Its county seat is Wheatland."