My kids' teachers had weird rules like this last year. They were not allowed to wear any kind of jackets in the classroom. One day the teacher sent DD10 (then 9) down to the nurse's office saying that it was hot in the classroom, and DD didn't want to take off her light fleece jacket, so she must be sick.
The nurse called me to ask me what the deal was. I told her that DD was not sick at home, and that as far as I am concerned, at age 9, DD was old enough to decide whether she was hot or cold, and that she would wear or remove her jacket as she needed to. I also told her I thought it was a little power play DD was pulling with her teacher, and that the best thing to do would be to ignore it. The nurse agreed with me and I didn't hear anything else about it.
I can understand teachers not wanting kids to wear big, bulky, noisy jackets, but a light jacket or fleece, come on!