Here's a tip for dealing with wet, muddy foot print on carpet. Sprinkle cornstarch over the foot print and let it dry. Once dry, vacuum up the cornstarch. In any case, mud is always much easier to remove when it is dry, if you try to clean it when it is wet, you just spread it around.
When you get muddy footprints in my house or car, sprinkle them with baking soda and let them dry. Once dry, vacuum up the dirt and then clean any leftover stain with Resolve or a similar carpet spot cleaner. If you try to clean the mud when it is wet, it will just spread it around and make the stain bigger.
To clean mud from carpet easier, let it dry then scrape what you can up with a brush, and vacuum.