Using wool curtain in gardenhouse
I am no expert either but I would think wool will be less prone to mold and mildew than other fibers.  It wicks away moisture more than most fibers.  I have many times had cotton goods get damp in storage and get musty / mildewed, but never wool blankets or coats.  

(Although moths do seem to prefer the wool.  You might have to treat it with something to keep the moths away.)  

It doesn't sound to me like your garden house is a particularly dark damp environment, so I doubt it would be a problem.