My door is locked if I'm not in the house so no parent is coming through if I'm in the yard. What a rude and disrespectful bunch you have!
I would address it head on. Send a note home -
"With the winter weather, heavy footwear often wet from snow or covered in salt, my wooden floor are being ruined by footware. Please remove your footwear when you enter my home. If you prefer not to do that, you are welcome to walk around the property to pick up your child when we are outside, or remain on the mats provided if we are inside. Your co-operation in this matter is both expected and required."