I live in the south and the moisture is enough that not only do my closets get mold, so does the plastic siding on the outside of my house. I treat both with bleach. Only my duck house, with the extra ventilation, is mold-free. Oh, and the crawl space is also mold-free, because I leave a large fan running continuously during spring, summer and fall to move the air around. That would be another option for your chicken coop - a continuously running fan.