Hooded jumpers should be part of school uniforms for the practical reason that they keep people warm. Having a hood to pull over your head helps trap bodyheat very effectively, particularly through covering the back of the neck as well as the head.
Robes with hoods have been part of fashion for a very long time. I've seen pictures of Jesus where he appears to be wearing some sort of proto-hoodie, which must be a persuasive argument given the number of people who display the motto 'What Would Jesus Do?'
When I was working in local government, where the fashions are extremely conservative, I relished the opportunity to add a sombre grey hoodie to my slacks and shirt uniform. However, the humble hoodie needs better PR. Images of rioters often show them worn for anonymity. Scenes like those from the 2011 riot in London have probably harmed the advancement and acceptance of hoodies.
Hoodies are great and should be embraced by everyone but particularly they should be part of school uniforms as they are practical, unisex, relatively inexpensive and class-less -- which isn't to suggest they have no class.
Above pic of Martin Luther King wearing a hooded jumper by Nikkolas Smith