Is our school being unreasonable?

Your school is not a state school, so it's not covered by whatever policies and decisions apply to the state schools.

I live where snow is a given.

The district sometimes closes all the schools, but there are times when some schools are open and others closed. It's largely based on whether the students, faculty, and staff can travel between school and home safely. The more walkers a school has, the more likely it is to close during a blizzard. If the city cannot keep the roads clear of snow or ice and issues a traffic advisory, that includes school buses and the schools who bus most of their kids close.

Here, the Catholic schools bus in nearly everybody, so they stay open so long as roads are in decent shape, at times when the public schools with their neighborhood walkers are closed.

As Chris P noted, the decision for your school is not made by any public school district but by whatever authority oversees Catholic education in the community. I imagine they evaluate risk the same way public schools do, but don't necessarily reach the same conclusion every single time.

that's horrible . It happens in New York schools as well, and it all has to do with the people in charge!

Catholic Schools are administered by the Catholic Church not the Local Education Authority - so they are not required to follow the same guidelines regarding school closures (usually based on the advice of the Environment and Highways departments of the Local Council; although in most cases it's based on whether enough staff can get into work and whether the school buses are operating ) as normal schools