I've been given a room at the Mage's College in Winterhold and the room and its furnishings appear to belong to me. Can I just continue to use this as my home or will things despawn or get stolen? I'm wondering if I should spend the money on a house given my free room here.

I'm actually quite interested in this myself, I had bought the house in Whiterun before I discovered Winterhold, so I already had a place xD

I was just getting ready to buy a house when I got to Winterhold, so I'm glad I saved my coin. Fortunately, coin is fairly easy to come by in this game.

Not sure, but, it's an easy thing to test out. Just drop a worthless item on your new bed or on your dresser. Leave, wait at least 24 hours, come back, and check. If you wanna be absolutely sure, wait 72 hours. Let us know what happens!