Snead grew up in Newport News, Virginia, the son of Hugh, a farmer, and Louise Snead. He attended Warwick High School, where he was a star three-sport (basketball, football and baseball) athlete. He won all six pitching decisions as a sophomore and junior, and he averaged 23 points in basketball as a senior, scoring 41 in one game. He split time as starting quarterback as a junior, then as a senior he passed for nearly 1,000 yards and 13 touchdowns. In a game against Hampton, he threw what would be the game-winning touchdown pass, then intercepted a pass on Hampton's next series to seal the outcome. He was named second-team all-state. He graduated in 1957.
Snead went to Wake Forest University, where he set 15 conference single-games, season and career passing records. His passing statistics with the Demon Deacons included:
In 1958, he was named the second-team All-Atlantic Coast Conference quarterback, and in 1959 and 1960 he earned first-team All-ACC honors. In 1960, he was named second-team All-American as a quarterback by UPI and the Football Writers Association of America.
In 1984, he was inducted into the Virginia Sports Hall of Fame.
He was named to the Pro Bowl on four occasions; in 1962, 1963, 1965, and in 1972, when he led the NFL in completion percentage and was second in passer rating. Ironically, he remains the last quarterback to win a game despite having a passer rating of zero, on November 14, 1976, against his former team, the Washington Redskins, winning that game while completing 3 of 14 passes for 26 yards in a game that had no touchdowns, winning 12-9. He retired after the 1976 season.
Snead was the 27th and then later the 29th head football coach at The Apprentice School in Newport News, Virginia, and he held that position for 10 seasons, from 1977 until 1984 and again from 1988 until 1989, when he resigned as coach and admissions director. After inheriting a team that was 0–9 the previous season, his coaching record at Apprentice was 46–41–2.