Reloaded in the garage for 20 years in Miami....never had a problem other than the sweat dripping off my forehead in the summer time. I did take precautions though, stored my powder in airtight containers, that was before everyone went to plastic ones that already are. I also stored all my loaded ammo in GI ammo cans to keep them somewhat dry. Becareful about storing you powder, primers and ammo in a garage where temps can hit 110 degrees plus.
I was always more concerned about the heat impacts than the humidity. One other method that might help you out; go to sears and get a craftsman roll around tool box base or "project center topped" version and mount your press on that. Roll it into the house for loading and roll it back out to the garage for storage. I've done that for years, have a dillon 550 mounted on one side and a rock chucker mounted on the other, with all the other goodies inbetween.
good luck,
graycg