I used to get that cold feeling, too sometimes. Not anymore. I think it might take a few months to adapt. But the real question is, are you sure you need to go this low carb? Do you do a carb refeed day here and there? There's a thousand ideas we will be throwing at you, don't get suckered by any of it - if this isn't working for you and some hacks don't fix it, try something else. I'm lucky, this worked well for me. So it's easy for me to say things like, "Give it time, etc."
Steak, eggs, potatoes - fruits, nuts, berries and forage. Coconut milk and potent herbs and spices. Tea instead of coffee now and teeny amounts of kelp daily. Let's see how this does! Not really had dairy much, and gut seems better for it.