There are 3 US Post Offices in Cochran County serving a total of 3,149 residents equating to 1,050 residents per post office. It's estimated that approximately 5,026 packages are handled across the 3 county post offices annually. Cochran County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 3,127. The county seat is Morton. The county was created in 1876 and later organized in 1924. It is named for Robert E. Cochran, a defender of the Alamo."