Butternuts is a town located in Otsego County, New York, United States. As of the 2010 census, the town had a population of 1,786. The Town of Butternuts is located in the southwestern part of the c…Butternuts is a town located in Otsego County, New York, United States. As of the 2010 census, the town had a population of 1,786. The Town of Butternuts is located in the southwestern part of the county, and is west of Oneonta.