When I entered the college in Winterhold, they gave me a room. It doesn't have a door. Are items left there...maybe in the dresser...safe?

Just don't leave them in the barrel.

I was wondering the same thing

On my 3rd character (a mage) I left everything in my room at the college. Separated them by type and put them in every container in the room. As long as you visit often you should have no problem with items disappearing. I utilized this room for a month before I got the Proudspire Manor in Solitude.

This.