When dealing with muddy paws on the carpet, just sprinkle with enough baking soda to cover the mud print and let it dry. Once dry, vacuum up the baking soda and dirt. If there is a light stain, spray with carpet stain remover and it should lift right up.
Mud is always much easier to remove when it is dry so never try to clean it when the muddy paw prints is wet. It will just smear deeper into the carpet fibers.
Howling for rainy days!