There are 6 US Post Offices in Carter County serving a total of 28,163 residents equating to 4,694 residents per post office. It's estimated that approximately 44,951 packages are handled across the 6 county post offices annually. Carter County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 27,720. Its county seat is Grayson, Kentucky. The county was formed in 1838 and was named for William Grayson Carter, a state senator at the time of its creation. The county seat is named for his uncle, Robert Grayson.