Winkler's audition for the Yale School of Drama was to be a Shakespeare monologue, which he promptly forgot, so he made up his own Shakespeare monologue. Out of a class of 25 actors, 11 finished. During summers, he and his classmates opened a summer stock theater called New Haven Free Theater, putting on various plays including "Woyzeck," and an improv night. The company put on a production of "The American Pig" at the Joseph Papp Public Theater for the New York Shakespeare Festival in New York City. In June 1970, after graduating from Yale, Winkler was asked to be part of the Yale Repertory Theatre company, which included James Naughton and Jill Eikenberry.