I teach UKS2 so 9-11 year olds.
We don't let them outside without their coats on and done up when it's cold or a bit drizzly.
Some will do it themselves through choice but many will tell you its not cold and they don't need them.
They're not allowed to leave the building without them on. If I wouldn't let my own child out in that weather without a coat, I'm not going to let someone else's out either.
But by the time they have walked down too the playground, most of them will have removed their coats completely.
.
They're often running around and playing football or whatever anyway so they're not actually cold even though the air is.
I also know the children and parents well enough to know which ones definitely want their children to wear coats and which ones don't mind them using their own judgement. I'll give an extra reminder to those children to put it back on but I can't physically do it for them if they don't want to wear it.
We also have a supply of donated, outgrown coats in school for the children whose parents send them in without a coat at all even when there's snow on the ground. We still can't force them to wear it.
We have in the past kept children in at playtime if they have no coat/refuse to wear it if its too cold but I can't imagine that would go down too well with parents either!
So it's untrue too say that schools do nothing about this. All the schools I've worked in have been similar.