We mostly deal with the insides of cars, but we're also interested in the whole package. This story from thecarconnection.com has good information about the need to wash ash residue from your car. In Idaho, August has seen weeks of smoke-filled air from wildfires and a good deal of that has wound up on cars.
According to the story, if water is allowed to mix with the ash on the car, it will create potassium hydroxide, which is similar to drain cleaner and will etch paint.
The best solution is to keep your car garaged, but that's not possible if you're out driving. A good car wash or at least rinsing it off the car daily is the next best option.