Snelling is a town in Barnwell County, South Carolina, United States. The population was 274 at the 2010 census. Snelling is located near the center of Barnwell County at 33°14′29″N 81°27′11″W / 33.24139°N 81.45306°W. South Carolina Highway 64 passes through the center of town, leading east 5 miles to Barnwell, the county seat, and west 1 mile to the east …Snelling is a town in Barnwell County, South Carolina, United States. The population was 274 at the 2010 census. Snelling is located near the center of Barnwell County at 33°14′29″N 81°27′11″W / 33.24139°N 81.45306°W. South Carolina Highway 64 passes through the center of town, leading east 5 miles to Barnwell, the county seat, and west 1 mile to the east entrance of the Savannah River Site, a nuclear reservation.