 Winn was first elected to the U.S. House of Representatives as a Republican from the Wyandotte and Johnson Counties-based 3rd congressional district in 1966, succeeding three-term congressman Robert Ellsworth, and would be reelected eight more times until his retirement in 1984.During his tenure, he served on the House Committee on Foreign Affairs and was a congressional representative to the United Nations.He was succeeded by fellow Republican Jan Meyers.