Winter was born in Ventura, California. He began his acting career in Ashland, Oregon as a member of the cast of the Oregon Shakespeare Festival. During the 1961 season, he played Claudius in Hamlet and stayed for an extended repertory season where he appeared in The Boyfriend and Rashomon. He went on to early successes on Broadway. Winter was twice nominated for Tony Awards as Best Supporting or Featured Actor (Musical). The first was in 1967, as Ernst Ludwig in Cabaret, then in 1969 as J.D. Sheldrake in Promises, Promises. He moved on to television, appearing on the daytime serials The Secret Storm and Somerset.

In 1973, Winter began his recurring role as Colonel Flagg on MAS*H. Flagg was a pompous and incompetent officer who was constantly butting heads with the doctors and nurses at the 4077th. The character was a fan favorite and Winter appeared in 17 episodes of the show.

Winter's other notable television roles included U.S. Air Force investigator Capt. Ben Ryan in season 2 of Project U.F.O. (1978–1979); and in Hollywood Beat (1985), 9 to 5 (1986–1988), and Herman's Head (1991–1994).

Winter also had a successful career in voice acting. He voiced characters in the animated series The Angry Beavers, Paddington Bear, and The Tick.

Winter died in 2001 at the age of 63 from complications from Parkinson's disease. He was married three times and had two children.