Horn began playing the piano at the age of four, the clarinet at ten, and the saxophone at twelve. He studied the clarinet and flute at the Oberlin Conservatory of Music in Ohio, earning a bachelor's degree. He gained a master's degree from the Manhattan School of Music.
Moving to Los Angeles he played with Chico Hamilton's quintet from 1956 to 1958 and became an established West Coast session player. He played on the Duke Ellington Orchestra's Suite Thursday and worked with Nat King Cole, Tony Bennett and others. He scored the 1959 animated television series Clutch Cargo.
In 1960 Horn recorded for Fantasy Records with Latin Jazz vibraphonist Cal Tjader (with drummers Willie Bobo and Mongo Santamaria) for the album Latino! (originally released in 1962 and later re-released with the same title in 1992.)
Horn became a practitioner of Transcendental Meditation. He attended training at the Maharishi Mahesh Yogi's ashram along with The Beatles on their 1968 trip to India. Following his experiences in India Horn's recordings moved from jazz to world and new-age music.
In 1970, he moved with his two sons Marlen and Robin from his first marriage to Lilian Yvonne Jourdan, and second wife Tryntje Baum to Victoria, British Columbia, on Vancouver Island. He formed his own quintet and recorded film scores for the National Film Board of Canada.
He was known for his innovations on both metal and traditional wooden flutes. Best known of his albums are his "Inside" recordings, which feature airy, echoing sounds created in places of spiritual importance. The series began with Horn sneaking a tape recorder into the Taj Mahal during a trip to India in 1968, (released as Inside) He was also with the Beatles at Rishikesh in the same year and continued later with recordings "Inside II" (1972), "Inside The Great Pyramid of Giza" (1976), and a return to the Taj Mahal in 1989. Horn later made similar recordings in a cathedral, in the canyons of the Southwestern United States with Native American flutist R. Carlos Nakai, and with orcas.
In 1998 he was able to record within the walls of the Potala Palace in Lhasa, Tibet. Horn was the first westerner to be granted permission to perform inside this massive structure, considered the spiritual nexus of Tibetan Buddhism. Horn returned to Tibet in 2003 to film on the holy Mount Kailash, where he scattered the ashes of his former travelling companion, Buddhist monk Lama Tenzin.
While well practiced as a jazz musician, many of his works defy such categorization. As well as the Inside series, he recorded other albums of jazz with musicians from a range of cultures and backgrounds including China and Africa.
With Cal Tjader
With Lorez Alexandria
With Nat King Cole
With Buddy Collette
With Duke Ellington
With Chico Hamilton
With Fred Katz
With Shelly Manne
With Ken Nordine
With Shorty Rogers
With Pete Rugolo
With Lalo Schifrin
With The Beach Boys