Cobham was served by three Prime Ministers: Sidney Holland (1949–1957), Keith Holyoake (1957 and 1960–1972) and Walter Nash (1957–1960). He was most careful to not comment on controversial matters, and had a good working relationship with all three. He was instrumental in setting up the Outward Bound outdoor education organisation in New Zealand, opening the Outward Bound school in Anakiwa near Picton in September 1962, which bears his name. He visited the school in 1966 and was pleased with the progress that had been made.