I'm here in central Virginia, less than a mile from the James River, and even closer than that to a pretty good sized creek that runs into it. Nothing special here for humidity I suppose, but a long way from Arizona.
I've never had a problem with a gun rusting, except once when I grabbed a couple with sweaty hands when moving. Those rusted before we got where we were going. No damage I could see, it just wiped off, but it made my hair stand up for a few seconds.
I clean mine after I get back from the range. Back when I hunted I cleaned those at the end of the season. These days I keep my handguns waxed with Ren Wax, but I really do that as a way to "fool with them" than I do because I worry about rust. I just like to wax them really. Then I keep them in silicone "gun socks" but I've used just plain old cotton socks in the past. They worked just as well as far as I could tell. I've also stored them in leather holsters and have never seen any harm.
I remember my Grandfather's Parker and Fox shotguns. He used them for duck and goose hunting out on the Bay, and for everything else from bunnies to bucks. He wiped them off with an oily rag after cleaning. I never saw rust on his guns. Wear yes. Rust? Never.