Greenwood is a town in Steuben County, New York, United States. The population was 771 at the 2020 census. A pioneer road was cut through the town in the 18th century, but no settlers remained in the town. The first permanent settlers arrived around 1820. Salt production was an early industry. The main industry today is deer hunting, for which the town …Greenwood is a town in Steuben County, New York, United States. The population was 771 at the 2020 census. A pioneer road was cut through the town in the 18th century, but no settlers remained in the town. The first permanent settlers arrived around 1820. Salt production was an early industry. The main industry today is deer hunting, for which the town claims to be the top deer-take town in New York State.