I tried the barn/tackroom approach, it did not like my tack. It just isn't feasible to attempt to build my dream climate-controlled and cat free tack room in my modified dairy barn. The only leather that stays outside is my snaffle bridle that I use every day, and even that lives in the house in the winter when I can't ride so much. I also give it a thorough wipe with a leather cleaner/conditioner wipe daily and after each ride. All my saddles have stands in my room, I carry them to the barn when I ride.
I agree, a good cleaning with saddle soap and a good conditioner plus a reevaluation of your storage plan is in order.