Snow was recommended to Sussex County Cricket Club by the Sussex player and coach Ken Suttle as a batsman because he was a "magnificent hitter of the ball", but that his bowling was "erratic and not very hopeful". He quickly developed as a fast seam bowler who could knock batsmen on the head with his short balls, but who batted at number ten. He first played first-class cricket in the Glamorgan vs Sussex match at Cardiff Arms Park as an amateur in 1961, taking 2/12 and 3/67 and making 12 in his only innings. However, it was not until 1964 that he won his county cap and became a regular in the Sussex side, by which time he had become a professional player. He helped Sussex to win the Gillette Cup Final against Worcestershire in 1963, taking 3/13 on his cup debut, and Warwickshire in 1964, when he took 2/28. In the 1960s Sussex had four seam bowlers and no spinners, which was excellent for the Gillette Cup and the green wicket at Hove, but not elsewhere. Snow believed this cost them the County Championship in 1963 (they came 4th) as several games drifted away on a turning wicket with only part-time spinners in the team. Once Snow was established in the side and a Test bowler he was used for long spells on unresponsive wickets and he gained a reputation for "not trying" and he occasionally refused to bowl. Snow berated "the Sussex committee for their lack of guidance, initiative, communication, drive and general handling, which affected the growth of the club and team spirit". They in turn were displeased that he saved his best bowling for England. Nevertheless, Snow took 883 wickets (21.30) for Sussex in 1961–77 and was by far their most successful bowler of the period.