As others have already said, heads really are damned if they do, and damned if they don't. I'm a teacher, and my instinct would be that schools should remain open if at all possible - I know how much of an inconvenience a sudden closure is for many parents. However, the situation with 'Snow Days' is far more complex than many people seem to assume, and every school is different.
In my experience, for every parent that complains that schools should be open because they can't find childcare/workshy teachers 'just fancied a day off'/'it wasn't like this in their day', there will be another, equally vocal, parent complaining that the school should remain closed because the playground is too icy/travelling in is too dangerous/the children might get stranded at school/little Jimmy can't possibly go outside in this weather.
The last school I taught at had a very 'old-school' head, whose mantra was that the school should remain open at all costs. We were pretty much the only school to stay open in our borough (I'm in North London). On these occasions, half of the kids wouldn't turn up because their parents wanted them to 'make the most of the snow', and many of those who did come in arrived without gloves, wellies and sometimes even coats. Some parents would stipulate that they wanted their child to remain indoors all day as it was supposedly 'too dangerous' for them to play outside. (Obviously some lucky staff members got to miss their break/lunch in order to supervise these children.)
And it isn't only about whether the children and teachers can get to school safely; one one occasion my school did open, but was forced to close down shortly afterwards because the council announced at short notice that they couldn't provide any school lunches. Another time we opened and then had to close at lunchtime because the heating broke down, which made things even more difficult for parents who then had to leave work to collect their children.
Even if the current CRB system were drastically overhauled, the idea of teachers turning up at their local school on snowy days sounds completely unworkable (unless we accept that on these occasions teachers are merely glorified childcare). As others have mentioned, every school these days has children with complex needs, something which is fine if one teacher is unfamiliar with the school, but absolutely not fine if the entire teaching staff has just turned up for one day. And (having worked as a supply teacher) children's behaviour towards unfamiliar teachers can be testing at the best of times, let alone if they're completely overexcited because of the snow
Having said that, I do realise how frustrating it can be when a headteacher fails to make a clear decision. I once worked at a rural school and our head spent so long faffing about that I was skidding driving down the road through a virtual blizzard before the call came through to say we were shut. It subsequently turned out that, while all the other staff had been struggling into work (some had already arrived at school and become stranded), our lovely Head was sat at home in his dressing gown with a nice cup of tea!
The answer is obviously clear, decisive action by the head teacher, preferably the night before, and with each school making the decision based on its own circumstances, rather than copying each other as often seems to be the case.