Admitted to Clare College on 14 January 1931 where he took Classics and graduated in Law.
In his student days, Greenwood developed a lifelong passion for mountaineering, scaling numerous peaks in the Alps, Dolomites, Tyrol, and Norway, as well as mountains closer to home in Scotland and Wales. He was elected to the Alpine Club at the age of 24. His mountaineering expertise proved crucial during his military service in the Second World War. He went on to marry a fellow-mountaineer. He celebrated his 80th birthday by scaling the 6121-meter high Stok Kangri Himalayan peak in Ladakh.
1940 - joined the Royal Artillery as a temporary Captain.
1943 - at a mountain warfare conference at Lochailort, Scotland, he was transferred to the New Zealand Squadron as a climbing instructor for mountain warfare. He accompanied the New Zealand Squadron in its ultimately doomed attempt to occupy the Italian controlled Dodecanese Islands. Escaping to Turkey, he went on to become a liaison officer for the Long Range Desert Group of a British brigade in Montenegro in 1945. In June 1945, he joined the Allied Military Government Organization in Austria, serving until March 1946. Shortly afterwards, he joined the Colonial Office. He was awarded the Military Cross in 1944.
1946 - Deputy Registrar of the High Court of Uganda
1947 - Registrar
1950 - Resident Magistrate
1952 - called to the bar at London's Inner Temple
1954 - Crown Counsel
1956 - served briefly as Solicitor General of Fiji
1956-1963 - Attorney General
1963 - Attorney General of Gibraltar
He later filled in as Acting Attorney General of Montserrat, as well as a legal adviser in Hong Kong. He was also to spend a year in Washington, D.C. as an adviser to the Telstar Conference
Married fellow mountaineer Rosemary Farmborough Howard in 1956. They had first climbed together before the war. Up until 1978, they together climbed mountains in New Zealand, Austria, Italy, Greece, Nepal, India and Peru. They both belonged to the Eagle Ski Club.