I will admit our winter's are not as cold, or even close to being cold, as yours.
However to me our winter's seem to be getting colder. Lot's of ice too
because of it. I have to walk Buddy 4x daily. Rain, snow, sleet and ice.
I should have been a mailman

He's on the larger size for a Yorkie
so I really have no choice. He's been trained to potty outdoors only.
Next time around I will be smarter. Pee pad trained when I can't get
her outdoors in bad weather. Walking one is enough for me. I have
to also chase him to get a coat and sweater on him. He hates clothes
and cowers like he's being beaten. LOL If your little one is small
pad training would be the route I would take without question.
I envy anyone who can do that in cold weather. It's truly a blessing.