That's why normally these choices are forced on the Schools Chancellor, consulting with the Office of Emergency Management, and the Sanitation Department (which operates the snow plows). I'm sure by the time the decision gets to the mayor, it's largely already been made. But that doesn't mean he won't get blamed! The decision can go wrong in two ways: either he can keep schools open, and the snow piles up so high that it becomes clear he should have closed them, or the snow melts by the end of the school day, and he gets blamed for keeping them closed. Lose-lose indeed!
As a public school student, growing up in the city, I always rooted for school closings. But in those days, they were pretty infrequent: anything short of a solid foot of snow meant you were going to have to put on your boots and march in. This wasn't so bad in elementary school and Junior High—most NYC kids go to local schools pretty close to home. But in High School, it meant a treacherous subway ride with a seven block walk on either side, just to arrive and find out that half the kids, especially the ones from Queens and Staten Island, hadn't bothered to come in and nothing was getting done anyway. I also remember one time at Stuy, during a Nor'easter, watching the Hudson submerge teachers' cars in the parking lot along the river, and realizing that they probably didn't want to be there either. But they came in, because NYC teachers are devoted to their jobs, and providing a safe, warm place for students during a storm is an important civic duty.
That's why, in well-run, heavily funded, socialist paradises like New York, we should err on the side of keeping the schools open. Especially if there is less than a foot of snow, and especially if the MTA and OEM keep the subways running. We should also go out of our way to thank the teachers who have to travel to work, and, if we drive, drive extra slow to avoid any accidents with kids travelling on the streets.
That sounds about right to me.