Make sure that it is entirely dry from the top and bottom. Take out all the furniture and get the mat. Lay it flat or have it hanged and let the top part dry. After a few hours, check if that portion has dried already then flip it over to expose the bottom part. Usually, the bottom part is synthetic and won’t absorb water so it should dry quickly. If you have a wooden patio, it is best to let space dry first to prevent trapping of moisture and collecting molds.
For environments like these, it’s best to stay away from natural fibers such as wool. Go for synthetic fibers like polypropylene. These are sturdy types and water resistant. You’d want a material that won’t build up mold and mildew over time.