Ozone is a powerful oxidizing agent, a class of chemicals that breaks down organic substances into their base components.
Ozone gas is produced by an ozone generator that converts atmospheric oxygen (O2) into ozone (O3). This ozone gas breaks down/chemically transforms smoke odor molecules embedded in the fibers of your garments into odorless carbon dioxide (CO2) and water vapor, thereby neutralizing the smoke molecule.
Ozone will neutralize smoke molecules. Ozone can also destroy mold and fungus. The issue with your coat is not smoke, mold or fungus. The issue is mustiness caused by prolonged exposure to moisture. As a result, ozone will do nothing to remove the mustiness.
Not only will ozone not work, but ozone is potentially harmful in situations involving moisture.
Here's why: When ozone comes into contact with water vapor it forms hydrogen peroxide which, in turn, can bleach fabrics. All garments deemed appropriate for ozone treatment must be completely dry before being subject to ozone treatment.