He led the Oratorio Society for 32 years, beginning in 1973, after the resignation of T. Charles Lee. In addition to continuing the chorus's annual Messiah performances at Carnegie Hall (a tradition that goes back to 1891, when the venue opened) and its regular concert series, Woodside conducted concerts in honor of Carnegie Hall's anniversaries. The hall's 85th-anniversary concert in 1976 resulted in a recording that won Woodside a Grammy award.

Woodside toured extensively with the chorus, and also made guest-conducting appearances with European orchestras. In addition to his position with the Oratorio Society, he was music director of the Westchester Choral Society, Manhattan's Park Avenue Methodist Church, Yonker's Temple Emanu-El, and the Birch Wathen Lenox School. He retired from Birch Wathen, after 40 years there, in June.

Born in South Carolina, Woodside studied piano and organ, and held his first musical job, as organist of a church in Georgia, while he was still in high school. He went on to study music at Kent State University, the Cleveland Institute of Music, and the Juilliard School.