There are 6 US Post Offices in Vinton County serving a total of 12,575 residents equating to 2,096 residents per post office. It's estimated that approximately 20,071 packages are handled across the 6 county post offices annually. Vinton County is a county located in the U.S. state of Ohio. As of the 2010 census, the population was 13,435, making it the least populous county in the state. Its county seat is McArthur. The county is named for Samuel Finley Vinton, a 19th-century United States Congressman from Ohio."