Her career has spanned a wide range of dramatic productions on stage, in motion pictures and on television. She studied acting at Centenary Junior College and Boston University, graduating from the latter in 1966. During her college years Winn acted in student productions at Centenary Junior College, Boston University, and Harvard College and summer stock for two summers at The Priscilla Beach Theatre, south of Boston. Shortly after college she joined the company at American Conservatory Theater in San Francisco, where she remained for four years under the artistic direction of william Ball.

In the fall of 1970 Winn left American Conservatory Theater to star opposite Al Pacino in the film The Panic in Needle Park, for which she won the Best Actress award at the 1971 Cannes Film Festival. Although she went on to do several more films, such as The Exorcist, she spent most of her career in theater.

She retired from acting in 1978 but returned to play Cordelia in The Tragedy of King Lear for KCET in 1983. She did not return to the stage again until 2011, when she played the lead in The Last Romance at the San Jose Repertory Theatre. For this performance, she was nominated for a best Actress award by the San Francisco Bay Area Theatre Critics Circle.