Smith was a native of Van Wert, Ohio, where he was a three-sport star at Van Wert High School, graduating in 1957. He earned an appointment to West Point, but transferred to Bowling Green State University a year later to pursue coaching. He played two-way end at for the Falcons, playing on a small-college national championship team as a sophomore in 1959; he won all-league honors as a junior and was team captain as a senior. Smith graduated from Bowling Green in 1962 with a Bachelor of Science in Mathematics, and later earned a Master of Education from Bowling Green in 1967.