Bleach on a cloth mixed with water 50/50 will clear this up. We had the same trouble with window sills in our home in WI. The bleach will kill all the mold as well as return the wood to a like new color. If the wood is currently stained with a color you may lose that and have to re-stain.
Wet the cloth, and blot at the wood. Keep a bucket of clear water and a clean towel for rinsing. You may need to blot and let it sit for a while to work into the pores.
WBCCI #5501 AIR # 49
1978 Argosy 28 foot Motorhome
Wise men talk because they have something to say; fools, because they have to say something. -- Plato