So I hope there is an actual player-designated room, in which you know the chests are safe storage. Never trusted the College.
That would be pretty awesome. At least in the case of Castle Dawnguard though, I'd imagine it to be more of a communal area - beds in one room, perhaps a chest at the end of each bed. This is all guesswork, of course.
But regarding the College, I've never had any problems with it. I think my Mage still has Ulfric's clothes tucked away in the wardrobe of his old room, actually ...