Cohen was exposed to folk music at an early age due to the interest of his older brother Mike, who was one of the early urban folk performers of the post-World War II era, playing with a group called The Shantyboys.
After graduating from Yale where he studied painting and photography, Cohen played at coffee houses in the New York area, meeting many fellow artists, including Mike Seeger and Tom Paley. They all had a deep interest in traditional folk, country and western music. This resulted in the formation of The New Lost City Ramblers in 1958.
Cohen helped discover many country and folk artists, most notably Roscoe Holcomb and Dillard Chandler. In the early 1960's, Cohen began a documentary film dealing with Holcomb's life and the general environment of the hill country. The film was released in 1963, "The High Lonesome Sound".
Some of his best known images document the Abstract Expressionist scene centered around New York's Cedar Bar; Beat Generation writers during the filming of Robert Frank and Alfred Leslie's "Pull My Daisy"; and the "old time" musicians of Appalachia.
He has compiled and produced several compilations of traditional American folk music for Smithsonian Folkways.