Coats /hats scarves - how do they manage?

[stirling]

Really strange question but I need to keep my new Year 7 DS warm, he's really susceptible to colds and flu.
He wears a blazer with a synthetic jumper underneath.
Has a short walk to school. But sits outside with friends for lunch. Weather bitterly cold at the moment, so this week I gave him an insulated waterproof jacket, a beanie and scarf to wear - but of course he's got to lug it around all day as the locker he's been allocated is a detour to reach and a couple of buildings away.

Jacket etc delaying him between lessons - I've told him to just wear it to and from school, and at lunch, but he's struggling to store it in a rucksack that's crammed with books/ packed lunch etc.

Any suggestions? Do you think buying him a thermal Base Layer would suffice instead of the coat? It'll be Base Layer, shirt, pullover, blazer.
Then just hat and scarf.

Any advice appreciated
Thanks

In my experience, no secondary school pupil would be seen dead in a coat. And a hat and scarf? If you want them to get beaten up, yes

My ds, who is unspeakably skinny, will wear a skin under his shirt if it's sub zero.

Don't bother with a coat but definitely give him a beanie to wear. It will stop heat escaping from his head at least.

I lived in Scotland until DD1 was 13. I kid you not, even when we had a foot of snow, NONE of the high school kids wore coats or jackets. It's not cool you know!!

Even down here in Dorset it's been pretty cold recently and I see the girls going to the local high school with their skirts rolled up so the hem is just below their knickers, ankle socks, and just a shirt. I feel cold just looking at them!!