He had a strong interest in economics, education, European unity, international relations, modern languages and Scottish history. He was appointed to the board of trustees of the National Library of Scotland in 1961 and his papers are held by the Library.
In 1919, Woodburn married Barbara Halliday, a teacher who was elected to the Edinburgh Town Council.[1][4] He was a member of the United Free Church of Scotland.[1] Woodburn died in Edinburgh on 1 June 1978, aged 87, after a car crash he was involved in when driving to visit his wife in hospital.[1]