Carter's first interest in the theatre was to be a set designer. As a youngster, he would make models of sets inspired by motion pictures and the occasional play he would see with his mother. Soon he would populate these models with cutout figures. This led to him creating dialog for the figures as he moved them around the set.
His professional career as a playwright began in 1965 at the American Community Theater with the production of the short play Terraced Apartment. This work would evolve years later into an expanded version entitled Terraces.