Over time the wetness can effect the finish, but it takes more time than most people would think if you use a good oil.
Stainless steel and plastic stock are pretty new inventions in firearms history.
The F&I war, American Revolution, war of 1812, Westward Expansion, Mexican/American War, American Civil War, Western Indian Wars, Settlements of Canada, (by the Canadians’ of course) opening up of Alaska, Spanish American War, WW1, the "Banana Wars", WW2 in both the Pacific and the European theaters, the Korean War, and other than the use of the M-16, the Viet Nam war, as well as countless millions of hunting trips from the days of wheel lock muzzleloading rifles and shotguns up until the 1980s were all done with carbon steel or iron gun parts and wood stocks.
Even the M-16 of Viet Nam had steel barrels, bolts and “guts” and of course, all the metal of the enemies weapons was of regular steel too.
With some attention to care and a good oil (I like Corrosion X) we all did ok with wet guns. Sperm Oil was often used in the old days.
I would not worry much about them rusting into uselessness now either.
Our museums are full of old guns that were used hard in terrible conditions and they are still serviceable today for the most part. Now they don't look new, and they would look "newer" if they were made of plastic and Stainless, but most are not rusted into uselessness even now.
Wetness is hard on finishes more so than dry weather, but it’s not as devastating as the new marketers would try to make us all believe.
Care and oil are your guns friends.