This area is accessed from Magdalen Bridge or from the other end out of the University Parks where the cricket team play. There used always to be a sign up proclaiming its private nature which must have been one of the most ignored precepts of all time!
The deer park lies alongside the River Cherwell which flows into the Isis [Thames] nearby. It really does contain deer and there is a story, which for all I know may be true, that there is a family where one per generation gets into Magdalen, shoots a deer with a bow and arrow and is then rusticated [expelled].
The Cherwell itself is the site of massive punting activity the night leading to May morning when it is impossible to move on the river for punts moored up to hear the pagan hymn.