There are 3 US Post Offices in Dawson County serving a total of 14,127 residents equating to 4,709 residents per post office. It's estimated that approximately 22,548 packages are handled across the 3 county post offices annually. Dawson County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 13,833. The county seat is Lamesa. The county was created in 1876 and later organized in 1905. It is named for Nicholas Mosby Dawson, a soldier of the Texas Revolution. Dawson County comprises the Lamesa, TX Micropolitan Statistical Area."