There are 10 US Post Offices in Hamilton County serving a total of 4,198 residents equating to 420 residents per post office. It's estimated that approximately 6,700 packages are handled across the 10 county post offices annually. Hamilton County is a county located in the U.S. state of New York. As of the 2010 census, the population was 4,836, making it the least populous county in New York. Its county seat is Lake Pleasant. The county is named after Alexander Hamilton, the only member of the New York State delegation who signed the United States Constitution in 1787 and later the first United States Secretary of the Treasury. The county was created in 1816 and later organized in 1847. Hamilton County is one of only two counties that lie entirely within the Adirondack Park (Essex is the other). Because of its situation in the Adirondack Park, any development in the county is severely restricted by the New York State Constitution, which designates the park as \"forever wild.\" There is no permanent traffic light in the county."