The reason why a cat does not drink milk when it is born and is cold may be because the kitten is too weak, has a disease, or cannot get milk. You need to help the kitten find a nipple. If the kitten cannot suck milk on its own, it is best to Artificial feeding to avoid life-threatening risks.
Tip:
You can use a bottle or syringe to feed the kitten goat milk powder, and prepare a blanket for the kitten to keep warm to prevent the kitten from catching cold and getting sick.