James pauses a moment, then takes off his own hat and scarf, handing them both to Anna.

"Here. At least part of you needs to stay warm." He doesn't fully understand how much of her is robotic now and would even need the warmth, but it looks like it's definitely the head at least. Plus, at least for him, the seam between flesh and metal is the most painful in temperature extremes. If that seam is around the neck for her then she needs the scarf way more than he does.