He attended Yale University, but left after his sophomore year in 1955 to originate the role of the navigator in the Broadway play No Time for Sergeants.

In the late 1950s and early 1960s, he appeared in few theatre roles and guest starred on various television programs, including four episodes of the CBS sitcom, Pete and Gladys.

He was cast as Bruce Carter, a 26-year-old college student (though he had already graduated from Yale in real life) who lives temporarily in Westwood, Los Angeles, California, with his aunt, Gladys (Cara Williams), and her husband, insurance salesman, Pete Porter (Harry Morgan).

When You're a Good Man, Charlie Brown was adapted for a Hallmark Hall of Fame television special in 1973, Hinnant reprised his role as Snoopy.

[12] In February 1990, archival footage posthumously showed Hinnant singing "Suppertime" in the Peanuts documentary You Don't Look 40, Charlie Brown!