Byrne had a feeling that Nabooru's refusal to wear warm clothes out in the snow wasn't due to stupidity, though he didn't know what it was. The air and the snow were very cold, and she could easily get sick, due to lowered immune activity, or get hypothermia in general. That wouldn't do.

"If you're going to stay out here," he said, "You should attempt to warm up."

He removed his jacket and offered it to her. "Here, I don't need it. I'm used to the cold, since I wasn't raised in an arid desert."

He wasn't raised in a cold environment, no, but he wasn't accustomed to incredibly high temperatures like she was. Surely the cold would bother her a lot more than it would him. Besides, he needed to build up resistance to the temperature anyway. He could easily do without the jacket.