In August 1962, Snowden became the commanding officer, 3rd Battalion, 1st Marines and later commanded Battalion Landing Team 3/1 aboard the for deployment to the Caribbean during the Cuban crisis in October 1962. From May 1963 until June 1964, he served with the 1st Marine Division at Camp Pendleton, California, as deputy G-4, logistics officer and later as assistant chief of staff, G-4. He was promoted to colonel in February 1964. In July 1964, he was assigned as deputy assistant chief of staff, G-4, Fleet Marine Force, Pacific in Hawaii. Ordered to South Vietnam in August 1966, he saw duty as a commanding officer, 7th Marines, and as operations officer, III Marine Amphibious Force. He was awarded gold stars in lieu of a second and third Legion of Merit for his service in Vietnam.