Snelders was born in Westervoort, Gelderland. He started his career with FC Twente but is mostly remembered in Scotland, especially for his spell at Aberdeen following his move for £300,000 in summer 1988. A successful replacement for Jim Leighton, he had a very good first season at Pittodrie, winning the Scottish PFA Players' Player of the Year in 1989. He saved Anton Rogan's penalty in Aberdeen's penalty shootout win over Celtic in the 1990 Scottish Cup Final. After fracturing a cheekbone in a collision with Ally McCoist of Rangers in 1991, he was unavailable for the club's vital winner-takes-all match against the Gers in May of that year, with inexperienced understudy Michael Watt unable to prevent a 2–0 defeat. Snelders had also played in the Aberdeen side that beat Rangers to win the 1989 Scottish League Cup Final, but tasted defeat against the same opponents in that tournament's 1988 and 1992 editions and in the 1993 Scottish Cup Final, and was the regular goalkeeper as the Dons finished runners-up to Rangers in five of his seven full league campaigns. Midway through the one of the campaigns in which the team was not challenging for honours, Snelders was sent off for an incident of violent conduct on the pitch; his reaction to a penalty being awarded to Keith Wright of Hibernian was to strike the forward to the head, followed by kicking the ball over the stand and out of the stadium. His makeshift replacement, defender Brian Irvine, saved the spot-kick, only for Aberdeen to miss a penalty of their own and concede the winning goal in the last minute. The other unsuccessful year concluded with a play-off to prevent the club being relegated for the first time in their history, which was averted. He made 290 appearances for the club in all competitions. Having fallen behind Watt in the Aberdeen order, Snelders moved on to rivals Rangers for £300,000 in early 1996. As a confirmed backup player, initially to Andy Goram followed by Lionel Charbonnier then Stefan Klos, he made just 18 appearances for the Glasgow club before he was released in 1999. He played two seasons at MVV before he retired from playing and became a goalkeeping coach in his native Netherlands with FC Twente.
