In 1963 I lived quite near our village school and so did the teachers, however I remember it being closed for weeks due to frozen pipes, outside toilets that had frozen and the solid fuel heating not working. My friends and I had great times playing on sledges.
It's not so much health and safety with school closures now it's the distance teachers have to travel to work, very few live near their schools these days. I know some who travel 40 - 50 miles every morning. If teachers are worried about icy playgrounds they will keep them inside so while the kids are there it is not a problem. If during the day the weather deteriorates it's not always easy for parents to collect them. Loads of parents now drop their kids off by car, keeping those drivers off the roads during peak times makes everything safer. I know it's not ideal but for those who have kids at home for a few days educate them yourselves. There is loads you can do - baking, reading, quizzes, feeding birds, card games etc. We still have snow but most of the schools were open today.