Mold and mildew can grow on outdoor surfaces due to precipitation and high humidity, and it will require more than a quick cleaning to get rid of them. But don't worry; it is still possible to clean mold on your wood furniture if the mold hasn't entered the wood too deeply. If you have a lot of molds, you might try using distilled white vinegar to get rid of it. After an hour, wipe the area with a damp cloth and then a dry towel to remove the solution.