Born in Opunake, Snell moved with his family to Waikato in 1949 where he attended Te Aroha College and became an all-around sportsman. He won several middle-distance running events in his hometown of Te Aroha, although some members of his new school lived in Ngāruawāhia. He attended Mount Albert Grammar School in Auckland, where he took up a wide range of team and individual sports, including rugby union, cricket, tennis, badminton, and golf. As a teenager, Snell excelled in tennis, and pursued the sport through appearances at the Auckland and New Zealand Junior Tennis Championships.