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.[1] He was succeeded by fellow Republican Jan Meyers.
Winn met his wife, Joan Elliott, while attending college and the two would be married for seventy-three years until her death in 2015. Together, they had five children; the death of their son Robert in 1983 played a part in the senior Winn's decision to retire from Congress. He lived in Prairie Village until his death on December 31, 2017, at age 98.[1]