I was aged 11 in 1963 and remember the big freeze very well. However, I can't remember our school ever being closed, and we had to go in every day. It was only about a 10 minute walk and I believe that, in those days, most of the teachers lived fairly locally and could, if necessary, walk to work, too.
I can remember my parents telling me that the 1947 freeze was much worse.
I think that is a huge part of the problem now. With the advent of almost universal car ownership, many people now live a significant car journey away from their place of work or school, so it is no longer a question of just getting your boots on, setting out a bit earlier and walking.
I do wonder whether things would be better from a commuting, general health, local community and lifestyle viewpoint if more of us lived within walking distance of our work and schools.