Because he was still studying in Rome in 1940 when Italy declared war on France and the UK, he was unable to return to New Zealand, and remained in Rome. After his ordination he completed his doctorate in theology with a thesis on Saint John Fisher. At the same time he and Fr. John Flanagan (another Auckland priest in the same situation as Snedden) became announcers for Vatican Radio, engaged particularly to broadcast weekly lists of Australian and New Zealand prisoners of war. Although the priests were not identified, one frequent listener to the broadcasts concluded that the readers must be New Zealanders because Māori names were pronounced with "such clarity and precision". Unofficially, code-named "Horace", Snedden, along with Flanagan (code-named "Fanny"), also became involved with an underground movement led by an Irish priest in the Vatican Secretariat of State, Hugh O'Flaherty, finding safe houses, medicines and food supplies for escaped prisoners of war who were hiding in the environs of Rome.