In 1956, Snowden met accordionist Dick Contino at a party given by actor Tony Curtis. In September, after a three-month acquaintance, Snowden and Contino were married. Contino's family, who were Catholic, originally objected to the marriage because Snowden was divorced, but they relented and attended the civil ceremony in a Beverly Hills hotel. Snowden and Contino had three children together, in addition to her two children from her first marriage. Snowden left acting after her marriage and the birth of their first child. She sometimes appeared with him, as a singer, in his nightclub acts.