Snowden was born in Cowling in the West Riding of Yorkshire. His father had been a Chartist, and Snowden joined the Liberal Party and followed his parents in becoming a Methodist and a teetotaller. While researching a speech on the dangers of socialism, Snowden instead became convinced by the ideology, and joined the Independent Labour Party. He became a prominent speaker for the party and wrote a popular Christian socialist pamphlet with Keir Hardie entitled The Christ that is to Be in 1903.
Also in 1903, Snowden married Ethel Annakin, a campaigner for women's suffrage. In 1906, he became the Labour Party MP for Blackburn. He also wrote extensively on economics and advised David Lloyd George on the 1909 budget.
Snowden was a conscientious objector during World War I. He lost his parliamentary seat in 1918 but was re-elected for Colne Valley constituency in 1922, and became Ramsey MacDonald's chancellor in the 1924 Labour government. He reduced some flat-rate taxes but did not implement the socialist measures he had previously proposed.
Snowden became chancellor again in 1929, during the Great Depression. He proposed reducing unemployment benefit in 1931. When this proposal was defeated by the Cabinet, he joined MacDonald in forming a National Government with the Liberals and the Conservative Party, which implemented the policy. For this, he was expelled from the Labour Party, and in 1931 he decided to retire to the House of Lords.