The Olympic Peninsula is a varied climate where both the wettest city (Forks) and the driest (Sequim) are located. The months that you are looking at storing end in the dry season ( July -Sept). With the MH under cover that would prevent damage from leaking. I would not worry too much about the humidity levels. If you are worried, maybe leave a few dry-eaze containers in it. As for as mice, that will be an issue wherever you store it. First make it as uninviting as possible by sealing any place they might enter, removing food products, etc. Lastly place some traps and poison under cabinets, bed, couch, etc.
I live on the peninsula and keep my MH uncovered, the roof vents opened (have the max air covers) and unheated during the winter. I have not had an issue with mold or mildew inside. I also have not had mice issues but do put out glue traps that I check occasionally.