Maybe it's sensory. I have a 9 year old who has no special needs or issues and he will frequently put on certain sweaters or jackets because he likes the feel of the inside material. He likes soft materials like velour. You can tell that he often picks what he wears based on what it feels like on his skin. And he has a favorite blanket that he wants to sleep under, but will take it off the bed and put it on the couch where he usually does on-line learning so that he can cover himself with it during school. It isn't a warmth thing because when class is over, he's fine running around the house in shorts and tee shirts or short sleeve, short pants pajamas.

The only thing I would suggest is talking to him about what he likes about the coat. If he can articulate what he likes about the coat, you might be able to find other clothes that will give him the same feedback and give him options. When I found out what my son liked about that blanket, we were able to get clothes that had the same feel and he can sometimes choose over the blanket.

My son does this. He does have some special needs.
I actually took away his hoodies, hooded coat, and bought him a coat without a hood. If he wants to wear a coat, it's fine, but I feel like a hood covering his face is distracting for his teacher and his classmates. Plus it just makes him look weird, and he has enough trouble fitting in already.

Have you seen him in short sleeves recently? When my DS was 12 i could not get him out of hoodies, and this was summer. I wrote it off as a tween thing (like shorts in the winter) but we figured out about a month later that he was cutting and trying to keep it covered. Since your son is favoring a particular item, not just long sleeves, I would think it unlikely... but I never would have expected it of my son either so thought I should suggest it.

Does he like the extra weight of the coat? Maybe some weighted clothing (not that he should wear it all day) or a weighted blanket for sleep would help?