She attended a small private girls' school and received a scholarship for daughters of clergy, which enabled her to enrol at university.
[1] As Greenwood graduated during the Great Depression, when paid employment was difficult to find, she initially took an unpaid position at architectural firm Gummer and Ford.
She also worked in the office of Auckland architect Horace Massey and assisted with the design of the Heard's factory in Parnell.
In Wellington, she began as an architectural draughtswoman for the Department of Housing Construction and was later promoted to the position of architect.
She worked on designing state houses, and was the first woman to be employed as an architect in the New Zealand public service.