[2] Greenwood was called to the Victorian Bar in 1951 and shared chambers with future High Court justice and governor-general Ninian Stephen for a period.

He was appointed Queen's Counsel in 1969, but according to the Australian Dictionary of Biography did not "achieve the material success that would have been his had he confined himself to the usual activities of a barrister".

He and his close friend Alan Missen were known as civil libertarians and opposed the Menzies Government's attempts to ban the Communist Party in 1951.

[1] Greenwood was nominated to fill a casual vacancy in the Australian Senate, created by John Gorton's move to the House of Representatives in 1968.

[1] Following the 1975 election, he was appointed Deputy Leader of the Government in the Senate, and became Minister for Environment, Housing and Community Development in the Fraser ministry.