There are 3 US Post Offices in Moore County serving a total of 21,705 residents equating to 7,235 residents per post office. It's estimated that approximately 34,644 packages are handled across the 3 county post offices annually. Moore County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 21,904. The county seat is Dumas. The county was created in 1876 and organized in 1892. It is named for Edwin Ward Moore, the commander of the Texas Navy. The Dumas, TX Micropolitan Statistical Area includes all of Moore County. Moore County history is highlighted in the Window on the Plains Museum in Dumas."