We are not much different! We have 3 acres fenced for the dogs, and 10 out back mostly fenced for the dogs...
They get let out.. and generally go to the back of the horse barn and poop as far away as possible.. generally on TOP of a snow drift! Clean up does not generally happen until we get a good thaw, and can find the little land mines.
Then they come running like the heathen they are, into the house...
Right now we have had warm afternoons, and they have been bringing their fair share of muddy paws in ( they go out with us during Ranch chores, feeding livestock, and Play/run, etc) and we sweep mop daily to keep up with it, thankfully we have hard floors thru the house.