I would tell her I understand that she used that door because it was cold and seemed like the right thing to do, logically, in the moment. The fact that they are making an example of the kids because of the safety threats is something the school wants to do to try to keep security tight, for good reason. I’d tell her it is just one detention and not the end of the world. It won’t affect her grades. It was just one silly mishap. She’ll remember to take the other door, should something like this happen again.