I have a puppy girl and every time we return from a wet walk I get her towel and say, wipe feet Charlie good girl, I have a friend who taught their dog to allow this and I remember thinking it was fab to see so I am doing it in hope it will work.
Mine go into a muddy stream in my local park twice a day every day, so I am used to dealing with 2 wet, muddy dogs.
I have an jet attachment on my hose that lives by the back door which very quickly disposes of any mud on their legs or tummy. They quite enjoy this and don't mine the cold water. Then I have a super absorbent towel bought from Pets at Home that I squeeze round their legs and tummy ( as Kendal says never rub or you will get matts) which gets nearly all of the water. This all takes me only about 5 minutes.
Unless they have been swimming or caught in heavy rain ( although they do have raincoats!) they are pretty much ready for the run of my house! I never worry about mud or dirt I don't think you can have 2 cockapoos and be obsessed about it! I am fairly house proud and I don't think anyone would call my house filthy, and I do have cream carpets! (Actually they are oatmeal which has a slight fleck in it, excellent for hiding the odd muddy footprint!)
My two get muddy from the back yard quite frequently (like any times a day) so it's not practical to really wash as they are back outside in an hour or two and right back to being dirty. What I've discovered is to lay a towel on the floor and put a high vault treat on it. They end up moving around and stepping or laying on it and dry off enough. That and tile floors. They dry quick. If especially muddy but not enough for a bath, I wait til they are dry then brush - dirt comes right out.