For a few years I fought an on-going battle with a box full of belts, holsters and the like as well as a few saddles, all with various stages of mildew and mold from storage in humid areas. Through lots of trial and error as well as taking some advice from some old timers, I found that a mixture of Borax and vinigar has yielded great results.
First off, I carefully brushed off as much visible mold from the surfaces as possible. Then using a horse spray bottle with the Borax/vinigar solution, I sprayed it liberally onto the pieces, virtually soaking them on the finished side, flesh side, and edges, then allowed them to dry while exposed to indirect sunlight. The sunlight will kill most forms of the mold, and apparently the Borax crystalizes and adheres to the fungus, thereby neutralizing it. (learned this with a google search).
Once dried, I reconditioned the pieces and the saddles with pure olive oil. This was also advised by the old timers. As the olive oil is not protien based as are many other leather oils, it will not promote molding, nor will it attract hungry leather-chewing critters such as squirrels and the like to your tack room.
So far, I've had about 95% success with some mold returning to a few pieces, which I will give the full treatment again in the spring.
To put that 95% into perspective, I saved a collection of over forty holsters that otherwise would have...I don't even want to think about 'otherwise'.
Good luck and let me know how this works for you.