Indeed, I'm wearing a hoodie right now and I do on most days because I live in a very cold climate. But I don't have the hood up, and I rarely do. If I go outside to shovel snow, I'll probably put a stocking cap over my head and then draw my hood up as a windbreak.

I haven't stepped foot in a high school since the early aughts when my foster son was a student, and I've never been a teacher, so I'm not going to pretend to know how this stuff works. But wouldn't it be a lot easier to have students take their hoods down than to make them remove their hoodies? I mean, after all, the garment is ubiquitous. I literally can't think of anyone I know who doesn't wear one sometimes.