Greenwood was born in Whitby, Ontario, Canada, to John Hamar Greenwood (1829-1903), a lawyer who emigrated from Llanbister, Radnorshire, Wales, as a youth, and wife Charlotte Churchill Hubbard, who was from a United Empire Loyalist family that had an ancestor who immigrated to Canada after the American Revolutionary War.

[1] He was educated at the University of Toronto and worked at the Department of Agriculture in Ontario before emigrating to England as a young man and qualifying as a barrister at Gray's Inn in 1906.

On the outbreak of World War I in August 1914 he served in the Department of Recruiting at the War Office, and when David Lloyd George formed the Welsh National Executive Committee to recruit a Welsh Army Corps for 'Kitchener's Army' Greenwood was appointed Lieutenant-Colonel to raise and command the 10th (Service) Battalion, South Wales Borderers (1st Gwent) in December.

He took the battalion to the Western Front in December 1915, but was recalled to serve as a Deputy Assistant Adjutant-General at the War Office in April 1916 before the unit saw serious action.

[2] As Chief Secretary, Greenwood was closely identified with the aggressive use of two specially formed paramilitary forces – the Black and Tans and the Auxiliaries – during the Irish War of Independence.

Lord Riddell, a close friend of Prime Minister Lloyd George stated that although Greenwood's life was in constant danger he "seems to be tackling his job with great fearlessness and to be giving the Sinn Feiners some of their own medicine.

Walter Spencer of Fownhope Court, Herefordshire, and wife Anne "Annie" Elizabeth Hudson, became Viscountess Greenwood.