I live on the Oregon Coast where EVERYTHING is wet, EVERYTHING molds, and the RATS eat EVERYTHING that isn't in a chew proof container. I use empty chest freezers, which I would assume work the same as an empty refrigerator. We store horse, cat, cow, rabbit, goat, chicken, turkey and quail feed in there. We have added a little shelf in a corner where we also keep little things like the salt and mineral blocks for the rabbits, treats, vitamins, empty egg cartons to fill and such. It works out great, everything is in one spot, dry and clean. We've been doing this for about 20 years.
We tried the empty metal garbage cans, but even those rust out on the bottom on the Oregon Coast unless you build a stand for them... It would be nicer for me to have a few separate garbage cans for the animals on the outskirts of the property, but that will be a "eventually" project.