If you have a refrigerator with a compressor it won't care or be damaged.
If you have a standard Propane/Electric absorption refrigerator it needs to be fairly level when it's running. If the refrigerator is off then it does not need to be level.
The post above about being level for the slides and draining the water for winterizing makes sense to me. I would make sure it was level before doing either if those things.
Aside from the absorption refrigerator or the other two mentions above your trailer can be stored off level with no damage.