If it gets cold and you feel like it’s doing harm, take it off. It’s possible that you might have gotten a size too small. Keep in mind that it will take time to get used to the Stealth, and especially the Corkscrew. Take it slow and steady, and try to understand how your genitals respond by trying different things for different lengths of time. I generally wear the innerwear with a spandex sleeve over it, and maybe a Sabre Skin. But, with that said, I’ve been using Stealth for a few years now, and my genitals have had a chance to get used to it.
Additionally, with the corkscrew, don’t start with it being tight, just put it on tight enough that it stays on when you’re sitting. Also, spread the pressure along your whole penis, not just behind the head of your glans. You’ll adjust to it more quickly, and it won’t slip off as easily. (That said, this also depends a great deal on the shape of your penis, whether it is tapered, and in what direction, etc.)
Be careful, and happy Stealthing 🙂