Wool is porous, so if you are using steam or spritzing the fabric with water or starch it will travel through a wool mat. I have some wool mats that are trivets and they hold moisture for days if dripped on. I do leave them on a clothing drying rack to dry out.
If you use steam or water mist or starch I would not leave a wool mat on top of a painted, wood, or other surface or material that could be damaged by moisture.
I would find some way for there to be good air circulation around all sides of a wool mat when not in use.