There is only so much you can do with controlling mud intake from your pets paws. Many pets go in and out all day, and when that snow melts and can cause real problems.
-One thing we tell a lot of people to do is to keep a towel right next to the door to make sure you can get as much off of their paws as possible.
-Another thing is to possibly keep a crate near the door with clean towels in it and when you let them in leave them in the crate for 10 minutes to dry their feet.
-On top of trying to do these things to clean their feet on the way in you should vacuum twice the amount you usually do. This will pull a lot of soiling out before it settles deep into the fibers.