Carter attended Rhodes College but took her undergraduate degree from the University of Memphis. Her career as an actress began in Memphis in 1961 when she played the role of Julie in the Front Street Theatre's production of Carousel. She moved to New York in 1962 and found work right away. Carter made her off-Broadway debut as Perdita in Shakespeare's A Winters Tale in 1963. She appeared as Maria Callas in the Broadway production of Terrence McNally's Master Class in 1997. She returned to Memphis in 1993 to play Blanche in a production of Tennessee Williams' A Streetcar Named Desire at the University of Memphis.
Carter took roles on Soap Operas in the 1970's. Designing Women launched on CBS in 1986 and ran for seven years.
She is survived by Hal Holbrook, her husband of 26 years.
UPDATE: As several readers have pointed out both schools have been renamed since Carter attended. Rhodes was Southwestern at Memphis and the University of Memphis was Memphis State University.