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Written dress codes can be a mine field when they get too specific. I had a manager once who couldn't confront a particular employee, so he wrote a dress code. It was so funny I used to take it to parties for people to read.
A thought, if she's cold now, what will she wear when winter sets in?
I am always freezing (and at 76F, I'd have my coat on too). When I was volunteering at Dress For Success, there was never any blazer and shirt combo that could keep me warm enough in the arctic A/C. Even my pleather jacket failed to insulate me properly. Silly as it sounds that is one of the main reasons I stopped volunteering there; it was that miserable. I really feel for anyone who is cold, but maybe you could at least get her to put her purse in a drawer. It sounds like she might not really be freezing, but is just a little stubborn, and maybe there's a bit of a power play going on (which would irritate me too)!
My coat has pockets in theory, but the keys ripped apart the lining, so I can't functionally use the pockets. Perhaps that is the case here? Or she doesn't want to keep valuables or medications in the pockets because things fall out, especially when you're sitting. Eating disorders, certain medications, etc. can make people cold, in addition to general biological dispositions.
Fashion related re: dress codes and how they can be difficult to write/uphold fairly: I was working at a suburban insurance office with a dress code when Capri pants became a huge thing one year (2000 I believe). Our dress code specified full-length pants... someone went spring shopping at a conservative store (Braemar? Canadian place now defunct) and asked the saleswoman to show her a single pair of pants she could buy for her office dress code... Not a chance. She emailed HR and they replied that they would not be updating the code. Another male colleague got called out for wearing collarless dress shirts. They were nice shirts and he dressed nicely overall, not hippy or anything, but I guess the code specified collars for men (which is actually rather sexist now that I think about it). We weren't in law or another area with a formal dress code, and we didn't see clients, so it all felt a bit much. And come to think of it not sure how I managed since I had no clothes, pretty sure I must have worn sandals for example.
Tl dr; dress codes can be arbitrary!
