I had a similar problem this summer- I left a good portion of my tack in one of my barns, more moisture in there than anticipated and my saddle, bridle, gloves, helmet, boots etc. all got moldy ( boo ).
For the leather, I washed it off with a damp cloth, and used a soft toothbrush to get into the seams and edges. Then I cleaned it normally with leather cleaner and left it to dry out by an open window. No idea if this is the correct way to deal with mold ( i've heard your supposed to treat it with a special cleaner and/or a vinegar like solution ) but my tack is doing fine now, no mold has re-grown and there's no damage.
" If the entire world was one big machine, I couldn't be an extra part. I had to be here for some reason." ~ Hugo Cabret