In this weather, if I had a young puppy - I would initially pad or paper train inside and then move to outside as the weather permits (there are books on how to do this). Once trained to go outside - then keep it that way.
Bailey is an outside pottier - and the colder the weather, the quicker the trip! She is two years old now. I remember last year, when it snowed, she didn't even make it off the deck
She'd drop trow right on the door mat and run back in. No problem, I just bought a new mat in the spring - lol. Thats no longer a problem this winter, tho.
Good luck!