I think this is a sensory issue and a genuine disability need.
As someone with an ASD, this is how I would experience playtimes:
Door handle to the playground, freezing cold - a shock that feels like pain. Jostling, noise - more pain. People shouting, so many voices, I can't make out what any of them are saying as it's all one wall of sound. They want me to join in, but I don't know who they are - I can't process the faces quickly enough. What are they saying? What do they want me to do? My balance isn't great, I can't join in the games as swiftly as they can. I am struggling to cope, it's overwhelming, I need to get away but I so want to have a friend so I try with all my might to cope with the sensory hell.
An adult comes over to me, she wants me to wear my coat. If I wear my coat, I will not be able to move properly/it's scratchy/it feels wrong/it's too hot (whatever the issue is for this young man). If that happens, I know that I won't cope at all as the pain of all the overload will be too much and I will have a meltdown or shutdown and it HURTS ME. Why do they want to hurt me every single day? Why can't they make it fair for me? "
His assumption is that the dinner ladies are trying to hurt him every day, and just won't stop.
His solution is clearly wrong, but it's a desperate cry for help. Please do tell the school what I've written here, if you think it would help at all. He's not being unreasonable, these are real sensory issues.
They may have to let him have a different routine for breaktimes, or give way on the subject of a coat. Is there a compromise of an extra layer underneath, a fleece, something that would work as well, for example?