Schools also have to worry about lawsuits from large numbers of parents if something goes wrong. The school I attended was notorious in the area for delaying opening or closing for the day if three snowflakes fell or somebody said the word "snow" really loud. It may have been an anecdote, but I was once told that, years earlier, the school chose not to close and a bus full of kids slid off the road and into a ditch, injuring students. The school became very cautious about snow after that.
It isn't just a matter of how much snow. Multiple conditions come into play.
One of the worst "snow days" in the decades I've lived here in central NC involved about 1/4" of snow.
No one had expected any precipitation, and so the brine trucks hadn't gone out the night before to pre-treat the roads. The daily temps had been cold enough for long enough that surface temps were below freezing.
Around lunch-time on that day "a few flakes" started falling. This was when lots of people thought it might be a good idea to go home early just in case.
The roads got busy.
Heat from traffic melted that little bit of snow that was falling ... and then it re-froze. Every single street and highway turned into a skating rink. School buses were having so much trouble staying on the road that some of them pulled over on the side of the Interstates, Accidents had blocked traffic everywhere and the DOT trucks couldn't get out to treat the roads. Some school kids ended up overnighting in shopping malls and area churches because they couldn't get home. It took all day through the next day to get everything sorted out, all the kids home, and all the roads cleared.
I can't describe how fast this happened, but this might give an idea. I was working on a job site that was close enough to my house that I could go home for lunch. I drove the three miles or so home with no problem.
Half an hour later when I headed back I almost didn't get there because the roads were so slick.
I don't blame schools for an abundance of caution.
Just as a side note, I grew up in WV and was quite used to snow. I lived within walking distance of school and never had to bus, but there were a few days I was able to ski to my high school, which was about six blocks from my house ... straight down hill. This is to say, my experience has made me very familiar with, even accustomed to snowy weather. That's just taught me to respect it.