Wolsey is a town in Beadle County, South Dakota, United States. The population was 459 at the 2020 census. The first settlement at Wolsey was made in 1882. A post office has been in operation in Wolsey since 1883, the same year the town was platted. The township was organized the following year, in 1884. The town of Wolsey was named for Thomas …Wolsey is a town in Beadle County, South Dakota, United States. The population was 459 at the 2020 census. The first settlement at Wolsey was made in 1882. A post office has been in operation in Wolsey since 1883, the same year the town was platted. The township was organized the following year, in 1884. The town of Wolsey was named for Thomas Wolsey, an English cardinal.