I think he needs to go outside and build up his endurance to cold. If you keep him warm up against you he will get used to your warmth, there for, I would suggest taking him outside for a few minutes every hour about 6 to 8 times an hour... Once he is more comfortable, you can inscrease the time intervals. His coat will slowly build up and his paw resistance also. It is hard, if possible when you put him outside, have him out on a sheltered side of the house where the winds arn't as strong. They do sell paw protectors as in slippers or even a liquid, I would not recommend these products because he needs to build his endurance.
Just dont stay out too long! 2 or 3 minutes will do it! Good Luck, with your new puppy!
Whats its name?