Winkler was born in Barmen, today part of Wuppertal, North Rhine-Westphalia, Germany, the son of a riding teacher. His father, Paul Winkler, died as a soldier during the last week of World War II. The boy was drafted as a Flakhelfer and was a prisoner of war for a short time. The house of his mother in Frankfurt was destroyed by bombing. He made money, to support his mother and himself, as a groom in the stable of the Landgravine of Hesse in Kronberg im Taunus. He was also a riding teacher of the Americans who occupied the area. He began an apprenticeship in a textile store in Frankfurt in 1948.
Winkler participated in show jumping competitions and won for the first time on 10 October 1948, in Hünfeld, on Falkner. A new Olympic Committee for Riding (DOKR) was founded in 1949 by Gustav Rau, who moved it to Warendorf. He called Winkler to join in 1950. In the morning, Winkler trained horses for the committee, in the afternoon he worked as a carpenter.
Halla was a horse that the committee intended for eventing. Rau found her unsuitable for the task and called her owner and breeder Gustav Vierling in Darmstadt to take her back. Vierling came and asked Winkler to take care of the mare, which he accepted. The mare became an important part of his equestrian career.
Winkler won his first German championship in 1952, but could not participate in the Olympic Games in Helsinki that year because he was classified as a professional due to his teaching in the 1940s. On an initiative of
Willi Daume , he was qualified as an amateur by the end of the same year. Winkler won the World Championship with Halla in 1954, again in 1955, and became one of the favorites for the 1956 Olympic Games. In 1956 the Equestrian Games were held in Stockholm, as the athletes and their horses were not allowed to travel to Melbourne due to quarantine restrictions. In the first round Winkler pulled a groin muscle at the penultimate obstacle after his mare took off early and threw him out of position.
Despite the pain Winkler decided to ride in the second round as the German team would be eliminated without him. After he was given tranquilizers Winkler found that he was comfortable sitting, but riding was difficult and painful. Any drugs that could reduce the pain enough to make him comfortable in the saddle also would reduce his mental capacity, and therefore, he was only given black coffee before his ride to try to help reduce his dizziness and double-vision. Halla apparently sensed that her rider was not right and performed the entire course clear with only steering from Winkler, and their performance won them the individual and team gold.
Hans Günter Winkler at the 2012 German show jumping and dressage derby in Hamburg
Winkler won five gold medals in jumping (in addition to the four individual medals with the German team) between 1956 and 1976, as well as a silver medal and a bronze medal. He is one of the most successful German Olympic athletes, third only to Isabell Werth and Reiner Klimke for gold medals produced in German equestrian competition. He was German Sportspersonality of the Year in 1955 and 1956. Winkler retired from jumping on 13 July 1986 with the conclusion of the Aachen tournament. Winkler worked as a trainer for the German Olympic teams, along with Paul Schockemöhle and
Herbert Mayer, leading them to success in Seoul in 1988. He consulted companies who wanted to sponsor equestrian sport, organized tournaments, and worked for the development of young riders.
He later published numerous books on riding and in 1991 founded the HGW-Marketinggesellschaft, a sports marketing firm that has helped produce various equestrian competitions. He was also a member of the German Equestrian Federation's Jumping Committee and helped to select the 2000 Olympic Team for Germany. The German Equestrian Federation announced his death in Warendorf on 9 July 2018.