i collect C&R guns. I have dozens of old broom mausers that have a leather frog on the wood butstock/holster.. other than regular handling marks onthe leather and the wood.. I don't notice any 'damage' the leather has done to the wood.
mind you i PROPERLY store and care for my guns.. so i don't leave them out in the rain or on a porch.. under the bed or in places elements can get to them. IMHO.. if too much moisture is getting to your guns.. your wood stock or leather parts are the least of your concern. better check that rusty bore and action
I keep damp rid and other moistre / humidity control methods in the palce i store my guns.. lotsa options available.. everything from pre-made to DIY dessicant packs.. damp rid chemical /water collectors, to electric dry rods..
too many ways to control moisture to let it beat you..