I think if you can live without one, I applaud you. I think if I was not a student I would try this. Actually, if you own property, you can bury things or put them in a "cellar." My grandparents had a cellar, they stay pretty cold (I don't know about Arizona though. I'm talking West Virginia and a part of Northern California that is extremely similar to Medieval England in climate).
I can see a cellar working here. I chose a first floor bedroom in my townhouse (I basically live in an 80s house, it's HUGE, we have a garage and everything, and two floors) and my bedroom is either freezing or a breath of fresh air compared to the floor with the living room and kitchen. We're almost underground.
As a vegan, certain veggies will last longer, and left-overs will last longer in a refrigerator. If I owned my home and property, maybe I would bury things or have a cellar like my grandpa (I was exposed to all of this as a child in WV where my grandpa grew all our vegetables and made our grape jelly and my uncles shot our meat, etc.)
Cellars are pretty cool. Literally. Ha ha! I'm surprised you can even get one in the AZ desert.