Ideally it should not. Fog is just air and water and both are odorless, tasteless and colorless. It is formed when the air temperature drops and water vapor that can no longer remain in solution begins to form droplets. There should be no odor. However, the microscopic water droplets can pick up microscopic particulates that are in the air. They could be from a factory or power plant many miles away, or wood smoke from your neighbor, dust from grasses, soils and trees, or even a particle or two from my house where I burned some leaves.