At home, I just don't see an issue. My DS is 16. Wears jeans most of the time. We live in Florida. Hot as heck here. Even I was wearing shorts and I almost never wear shorts. I get cold very very easily. Like the slightest breeze will give me a chill and then my teeth chatter and it is 90 degrees outside. Yeah, crazy.
At school...first, I would talk to the school. See if she can wear sweats. Find out the reason behind them only wearing shorts for gym. That sounds ridiculous. If they won't bend and let her wear sweats then she has to dress for gym in shorts. IF she chooses not to dress then she faces the consequences. One is failing gym class. The other would be a permanent grounding with extra chores to keep her busy until she decided to comply.