First, I have to ask about your 4yo: Did the child suffer any ill effects? Toes frostbitten? permanent damage? I would guess not.
I sit firmly in the camp that kids will come in if they're cold. I have coats, etc. readily available for my dc. I tell them to wear appropriate clothing. But, if they choose to go out w/o sweater/coat/shoes/hat when *I* think it is cold, so be it (my youngest is 4). They'll come in if they're cold. They may come in crying from the cold, and maybe they'll learn a lesson (listen to mom, cold snow hurts bare skin). If they are old enough to put their own clothing on, they are old enough to decide if they're cold or not, is my motto.
From your post, I think maybe I'm your neighbor, cuz I'm sure I DO bug my neighbors in a miriad of ways!