I too prop the fridge open and put a couple mouse traps in the trailer. I put one in living area and one in cargo space. Be sure to take all food out, clean the trailer and wash the bedding.
I haven't gotten any bugs, but I think spraying the landing gear and such with bug killer is a good idea....mine sits in our garage when not being used, but still could get em.
I've heard run the genny with a decent load once a month. Something about keeping the moisture out of it. I don't think its as big a deal here in Colorado as it would be in a humid climate like FL. A decent load would be your A/C, so run it too once a month. Daily would be overkill.
I have a battery tender that I often hook ours up to in order to keep the batteries charged. Its not just a charger...its a Battery Tender.
I flush our waste tanks before storage and put in a few gallons of water and the normal tank treatment. In the winter, I add RV antifreeze and of course I winterize the rig.
I try to move mine a couple times each winter to hopefully help prevent tire problems.