As a young man Haefner went to work in the auto industry as an employee of the Swiss division of General Motors Corporation. He eventually moved to England where he acquired an automobile franchise before returning home to open a Volkswagen dealership. Recognizing the important role a computer could play in his growing chain of dealerships, in 1957 Haefner became one of the first in Switzerland to import an IBM system for Business use. This led to his 1964 creation of Automation Center A.G., a computer services company in Zurich. In 1976 he expanded operations to the US and, after merging his company with Russell Artzt's and Charles Wang's publicly owned software company, Computer Associates International, Inc., in 1987, Haefner was CA's largest individual shareholder until his death. He continued to own AMAG Automobil- und Motoren, a highly successful Swiss automobile dealership chain. Until his death, at age 101, he was the oldest person worth more than a billion dollars.

In 1962 Haefner purchased the 440-acre (1.8 km) Moyglare Stud Farm near the town of Maynooth, County Kildare, Ireland. His thoroughbred racehorses have won numerous Group One and British Classic Races in England, Ireland, and France as well as important races at other venues in Europe, North America, Japan, Australia, and Hong Kong.

In 1975 the Curragh Racecourse honored Moyglare's contribution to Irish racing by naming a Group I race the Moyglare Stud Stakes. In 1988 Trinity College, Dublin awarded Haefner an honorary doctorate for his services to the Irish bloodstock industry and for his contributions to education in Ireland.

In the United States Moyglare's racing stable was handled by trainer Christophe Clement while Dermot K. Weld is the trainer in charge of its European operations. In 1991 Weld became the first European-based trainer to win a race in Hong Kong when Moyglare's colt Additional Risk won the Hong Kong Invitational Bowl at Sha Tin Racecourse.