The cold thing is normal while fasting. Fasting slows the metabolism. The last MC I did in cold weather I swore I would never do it again. But here I just finished a 36 dayer in late December and yes I was cold most of the time too. I had issues with dry itchy skin from the heated rooms dry air. Took care of that though by rubbing on some virgin coconut oil. Wore fleece and a hat thoughout the fast even while inside the house. I live in the SE where the temps are mild compared to the northern latitudes so I feel for yous guys up nath.
Just stay bundled and wear a hat and warm socks. Most folk will feel the cold mostly on their hands and feet so you can bet I had my wool socks and warm house booties on all the time. It's all bearable though so just throw on and extra layer and press on.