It doesn't matter if you and "plenty of people" don't mind, the important part is that the majority of people do mind, and will not cycle in cold winter rain.
I bike with my kids in -12C. You dress like they're going sledding or skiing. It's fine. If you live in a cold climate, you just have that stuff anyway.
Why, it's much better for the kids to just take the bus, it's more practical and easier, and they don't have the risk of sitting cold and wet in school, what's the point of stubbornly cycling in shitty weather
I also had to cycle my whole childhood to school, and I don't see the point at all, it just felt like some kind of unnecessary punishment and some creepy amish like way of being against technology