Some dig a path in the snow & put a coat on their pup to go potty outside in the winter here in Michigan.
I've always pad trained as it's the most convenient for me with my lifestyle & work hours. As to not knowing the difference between the bathtub & living room carpet.... I've trained my dog where to go, not just on what to go. Her potty area is in one spot in the house, and that is the only place she gets rewarded (a treat) for going. She picked up on the training very quickly and doesn't go potty anywhere else in the house. Just like kids get trained to go to the bathroom to potty and don't just squat and go anywhere in the house.