First, take the time to check the coat tag. Each coat has its cleaning specifications!
Run your machine on the delicate program, at medium temperature (lukewarm).
During the wash cycle of the coat, you can clean the fur of the coat.
Dampen a clean cloth without using detergent, and clean the fur gently in the direction of the fibers, insisting if the stains persist. Let dry. Once dry, brush your fur in the direction of the hairs so that it regains its original appearance.
Some clothes, such as non washable fabric, or pale colored once, can be protected from stain and dirt with a fabric protector.
Product like scotch guard spray for fabric can be a good idea. So if you are scared of pale winter jacket, don't! Use a protector in a spray formula to assure stain won't stick to your favorite coat.