Hinson was born in Tylertown, Mississippi, and he graduated from the University of Mississippi in Oxford. Hinson was an aide to Representatives Charles H. Griffin, a Democrat, and Thad Cochran, a Republican. He was elected to the House of Representatives as a Republican in 1978, rising from relative obscurity. Cochran vacated the seat because he was elected to the U.S. Senate.
During his re-election campaign in 1980, Hinson admitted that in 1976 while an aide to Cochran, he had been arrested for committing an obscene act, exposing himself to an undercover policeman, at the Iwo Jima Memorial in Arlington National Cemetery. Hinson denied that he was homosexual and blamed his problems on alcoholism. He said that he had reformed and refused to yield to demands that he resign. He won re-election.
Hinson, who was married to Cynthia Hinson, was then arrested on February 5, 1981 and was charged with attempted oral sodomy for performing oral sex on an African-American male employee of the Library of Congress in a restroom of the House of Representatives. After his arrest, Hinson was charged with sodomy, a felony at the time carrying a maximum fine of $10,000 and sentence of 10 years in prison.
But the United States Attorney's office reduced the charge to a misdemeanor, which carried a maximum one-year penalty and a fine of $1,000. In explaining the reduction in the charge, Percy H. Russell, deputy director of Superior Court operations for the United States Attorney's office, said it was office policy that homosexual acts between consenting adults be prosecuted as misdemeanors. Hinson pleaded not guilty to a charge of attempted sodomy the following day and was released without bail pending a trial scheduled for May 4, 1981.
Hinson checked into a hospital in the Washington area shortly after his court appearance, according to his office. Marshall Hanbury, Hinson's administrative assistant, said that the Congressman had voluntarily admitted himself to a hospital.
He resigned on April 13, 1981, early in his second term. He said that his resignation had been "the most painful and difficult decision of my life." He was succeeded in Congress by Wayne Dowdy, a Democrat, who won the special election held in the summer of 1981.
He later acknowledged his homosexuality and became active in the gay-rights movement. His marriage ended, and he became an activist for gay rights. He helped to organize the lobbying group "Virginians for Justice" and fought against the ban on gays in the military. He also was a founding member of the Fairfax Lesbian and Gay Citizens Association in Fairfax County.
He never returned to Mississippi but lived quietly in the Washington area, first in Alexandria, Virginia and then Silver Spring, Maryland. Hinson also disclosed that he survived a 1977 fire that killed nine people at the Cinema Follies, a Washington theater that catered to a gay clientèle. He was rescued from under a pile of bodies - one of only four men who survived.
Hinson died of respiratory failure resulting from AIDS in Silver Spring at the age of 53. Hinson's body was cremated, and the ashes were buried in Tylertown after a private service. Hinson, by then divorced, was survived by a brother, Robert Hinson, in Gulfport, Mississippi.