At an early age, Henry began studying classical violin, then switched to woodwinds. He proved himself gifted and was selected to play with the Corpus Christi Symphony Orchestra in Texas while still in high school. Before being drafted into the Army in 1952, Henry graduated from Del Mar College where he majored in music. In the Special Services branch of the Army, he was involved in entertaining troops in Europe and England, including a Tribute to Gershwin concert with the Stuttgart Symphony Orchestra.
After his Army duty, Henry toured the United States and Canada, developing his own highly personal style. While living in Toronto, Henry and his group became the mecca for visiting musicians, including Benny Goodman on one occasion. Bobby Hackett advised him to get in touch with Lawrence Welk, and after listening to his recordings, Mr. Welk hired him immediately.
Henry made countless personal appearances performing and conducting in jazz festivals, state and county fairs, conventions, supper clubs, symphony pops concerts, etc. He has appeared as a soloist with Jack Teagarden, Bob Crosby, Mel Torme, in a Bobby Vinton TV special, on the Tonight Show starring Johnny Carson, and ten years on the Lawrence Welk Show.
In 1982, Henry played a special concert on the steps of the US Capitol with the US Army Band. In 1993, Henry, along with Texas saxophonist David Caceres, was invited to perform on Riverwalk Jazz to pay tribute to his cousins Emilio and Ernie Caceres.
Henry Cuesta died December 17, 2003 at the age of 71 at his home in Sherman Oaks, CA.