In my humble opinion, closing school has nothing to do with regulating society. Every decision everybody makes anymore has to do with a fear of litigation. If they have school on a questionable day and a kid wrecks on the way to school the parents are likely going to take a shot at the district. I'm a hard core conservative, but the private sectors lust for lawsuits has brought a lot of this fear upon ourselves.
Schools handle this legally by saying that it is always the parents choice if they want to send their kids during bad weather. Therefore, no liability on the schools. We don't pay them boys/girls in the fancy suits for nothing.