If most of it is alloy, a bike should be able to get you through a few years without the metal parts (chain, derailleurs, screws, bolts, etc) rusting up too badly if you keep it well-covered.
Eleven81 Nylon Bike Cover Black | Bikewagon
Feel fortunate that you do not have to contend with -17C temperatures.
In your favor, I think your college is being entirely unreasonable for not allowing bikes in.
To answer your question, if you feel that extra gears would help, don't worry about them freezing up. Just keep everything covered. In my neck of the woods, I have had to resort to a propane torch to get locks, derailleurs unfrozen. It works.