There are 10 US Post Offices in Washita County serving a total of 10,851 residents equating to 1,085 residents per post office. It's estimated that approximately 17,319 packages are handled across the 10 county post offices annually. Washita County is a county located in the U.S. state of Oklahoma. As of the 2010 census, the population was 11,629. Its county seat is New Cordell. The county seat was formerly located in Cloud Chief. The county was created in 1891.