There are 8 US Post Offices in Medina County serving a total of 40,013 residents equating to 5,002 residents per post office. It's estimated that approximately 63,865 packages are handled across the 8 county post offices annually. Medina County is a county located in the U.S. state of Texas. As of the 2010 census, its population was 46,006. Its county seat is Hondo. The county is named for the Medina River. The Medina Dam, the fourth largest in the nation when completed in 1913, is listed on the National Register of Historic Places. The irrigation project, creating Medina Lake, was built by 1500 skilled workers who worked in shifts operating 24 hours a day to complete the dam in two years. Medina County is part of the San Antonio, TX Metropolitan Statistical Area."