After receiving a master's degree from Middlebury College in 1947, Carter returned to Milton Academy, where he taught French, German and Spanish until his retirement in 1979. He also founded the school's Ski and Mountaineering Club, which has become the H. Adams Carter Outdoor Program. Carter often used his second home in Jefferson, New Hampshire as a base camp for school trips to the White Mountains.
Carter served as an officer of the American Alpine Club from 1954 to 1958 and as editor of the American Alpine Journal from 1960 to 1995. Under his tenure as editor the Journal became one of the pre-eminent worldwide journals of record for mountaineering. He continued to participate in mountaineering expeditions, including one to survey Ojos del Salado (6,893 m) in 1956, several trips to the Cordillera Blanca in Peru, and a second expedition to Nanda Devi in 1976, which he co-led with Louis Reichardt and Willi Unsoeld.
Due to his long work as editor of the American Alpine Journal, Carter became an important chronicler of mountaineering.[2]
He was married to Ann Brooks Carter (1918-2012), also a climber and mountaineer.[3]