I doubt the chair would may any noise if cold. I can stick mine in the garage tonight and the next few days and test. Although we're only in the 30's. But I sat in it on several hunts and nothing ever made even the smallest creak.
I'm obsessive/OCD about noise when deer hunting, as many are. Be it clothing, boots, creaky limbs, a squeaky shelf plate, finger tab, chair, whatever, I won't tolerate noise. That's especially true when hunting natural cover, on the ground, with light weight traditional bows at extremely short ranges. There's no room for noise at 8-10 yards on the ground. That said, I just can't see this chair causing any noise issue under normal cold temps. Now, temps in the dead calm single digits and below can just about make wool noisy, so anything is possible in extreme cold temps.