There are 6 US Post Offices in Sublette County serving a total of 10,255 residents equating to 1,709 residents per post office. It's estimated that approximately 16,368 packages are handled across the 6 county post offices annually. Sublette County is a county located in the U.S. state of Wyoming. As of the 2010 census, the population was 10,247. The county seat is Pinedale. It is a sparsely populated rural county in western Wyoming, along the Green River."