Humid conditions?
I've really only had humidity related issues in 2 areas:
A> Waterfowl hunting. Of course, you are doing this in very moist conditions, quite often in awful weather conditions. Honestly, I found that the only special precautions necessary were to be sure that the shotguns were not dry on the surface, a light surface oiling is sufficient for protection. Or, use the silicone cloth. Then, after the hunt, a through cleaning is in order to remove all traces of moisture -- let common sense reign.
B> Military. Ok -- this was the acid test. Literally, the worst conditions imaginable. Corrosion was inevitable, and a constant battle to prevent. This was in the days before CLP, we only had LSA, and we had to slather that stuff on making sure that we weren't obstructing the bores of our weapons. We squirted that stuff directly into the actions of our M-16s which didn't seem to hurt anything at all -- for that matter, that was official SOP. We just had to make sure that the bore wasn't obstructed by LSA or anything else like mud or water. Again, when we were back in "normal" garrison conditions, we had to throughly clean & oil the weapons, which of course meant that we were getting rid of any latent moisture -- along with the inevitable corrosion which we were constantly plagued with.
Other than that, I really haven't had to do anything special to my weapons when dealing with humid conditions -- just my normal, run of the mill post-shooting maintainence seems to suffice.