Harry Winkler attended the University of Florida where he played basketball. He then joined the US Army where he learned handball and made the US national team. In addition to the 1976 Olympics, Winkler played for the US at the 1974 World Championships and was an alternate on the 1972 Olympic team. He later became a schoolteacher at Forest Hill High School in West Palm Beach, Florida, where he had attended high school, and retired from that profession in 2009 after more than 30 years teaching. In 1981 Winkler was inducted into the Palm Beach County Sports Hall of Fame.