Quidditch Through the Ages gives the following information about Quidditch referee qualifications:
The effective Quidditch referee needs to be more than an expert flier. He or she has to watch the antics of fourteen players at once [...] In Britain, Quidditch referees are selected by the Department of Magical Games and Sports. They have to take rigorous flying tests and an exacting written examination on the rules of Quidditch and prove, through a series of intensive trials, that they will not jinx or curse offensive players even under severe pressure.
Quidditch Through the Ages - page 31 - Scholastic Books - chapter 6, Changes in Quidditch Since the Fourteenth Century
Yet, in Philosopher's Stone, Snape referees the Gryffindor/Hufflepuff game:
‘Will you stop messing around!’ [Oliver Wood] yelled. ‘That’s exactly the sort of thing that’ll lose us the match! Snape’s refereeing this time, and he’ll be looking for any excuse to knock points off Gryffindor!’
George Weasley really did fall off his broom at these words. ‘Snape’s refereeing?’ he spluttered through a mouthful of mud. ‘When’s he ever refereed a Quidditch match? He’s not going to be fair if we might overtake Slytherin.’
Philosopher's Stone - page 159 - British Hardcover - chapter 13, Nicholas Flamel
One of the things that seemed to differentiate Snape from James Potter was James's status as a very good Chaser (no, he wasn't Seeker) for Gryffindor, and Snape being kind of gangly, unathletic, and bookish.
Did Snape play Quidditch while he was a student at Hogwarts?