Woodward won many beauty contests as a teenager. She appeared in theatrical productions at Greenville High and in Greenville's Little Theatre. She played a major role in "The Glass Menagerie", directed by Robert Hemphill McLane at the Little Theatre. She returned to Greenville in 1976, to play a starring role in another Little Theatre production of "The Glass Menagerie". She had first returned in 1955 for the premiére of her first movie, "Count Three And Pray", at the Paris Theatre on North Main Street. Woodward majored in drama at Louisiana State University. She then moved to New York City to perform on the stage.