Steinkraus competed for the United States on five Olympic show jumping teams between 1952 and 1972 and served on many Nations Cup teams as well. He was fourth individually at the 1960 World Championships in Venezia, Italy, riding Ksar d’Esprit.
Steinkraus retired from active competition in 1972, but he continued to serve the sport in an administrative role. He was elected president of the USET in 1973, became its chair in 1983 and then chair emeritus in 1992. He was a director at the American Horse Shows Association (now USEF) for more than 40 years and judged at Olympic Games, World Championships, World Cup Finals and Pan American Games. He was president of the FEI World Cup Committee for 10 years.