I am not used to the cold (and doubt I ever will be). I haven’t been here in the frozen north for long- this being my second winter here (Kansas- bleh) and previously being from South Carolina then Guam (moving from 80s-90s year round to freaking highs of 16 last week is rough!) and my poor puppy who is an almost 10 year old, 108 pound labrador mix feels the same way.
When it gets cold he goes in the backyard (what little we have, living in a townhouse) and does his business as quickly as possible then comes back in for warm water and to curl up by the fireplace. One thing about the cold weather is that it makes it much easier to keep the yard clean when the poop freezes on impact. 
When he really needs a walk, my delicate little flower of a puppy wears his coat (fleece lined, fake leather on the outside) on very cold days or a sweater on just “chilly” days and has been convinced to wear boots in the snow, but he doesn’t really like them so mostly it is just warmies when he gets inside (and he does let me know when he wants his water warmed (or iced in the summer).
You walk the little shits. They’re dogs, and they’ll be fine.
Now, we had a Chow/Shepard mix, so he was pretty damn fluffy anyway, and the great thing about walking your dog in the snow is that they get tired really quickly if you walk on the sidewalk and they cavort in the snowdrift, even if they’re still in the puppy-energy phase of life.
That was Eastern Oregon at maybe 5000 feet, so winters got down below zero but the real fact of life was that the rainshadow effect dumped tons of snow on us.
My partner’s dog will not foul his home territory and will not defecate in the yard or anywhere on our property. He extends this courtesy to places he visits too, so you can have him play in your yard with your kids and not worry that someone willl step in poop. This means he is always walked.
As PlanB has said, it’s no different than the necessary Point A to Point B walks that are required in any other normal day-to-day business. We have to walk to the subway or streetcar, or we have to walk to the corner store, or we have to walk around outside to shovel the walkway. Walking the dog is no different. It’s not like we never go outside in the winter.
The other side of the coin, of course, is the situation of people who live in hot climates and have to emerge from the air conditioning when it’s 95F out with 98% humidity.
I’m reminded of a resident physician I worked with who told me about being out for a summer walk in the early afternoon in Houston with his wife and child. A police officer driving by stopped to ask if they were all right.
Since he was from Bangladesh, it wasn’t much of a problem. But normal people generally don’t go for long summer walks in Houston except out of necessity. And I imagine that taking your long-haired dog for an extended hike in such weather would require special preparation.
Weezy starts shivering if he doesn’t have a sweater on him when it goes below 40. In the mornings, he’ll run around the yard (3ish acres, fenced) and try and see if any of his girlfriends (neighboring dogs) are around. He runs for about ten minutes, pees, and comes back in. In the evenings he’s walked 30-45 min. If he’s rambunctious, we’ll tell him to “run”, which means running about 30 feet worth of playroom + hallway until he gets tired.
My mother hates the cold - I pumped gas for her when I was under the legal age limit - but she bundles up to take him out religiously. If the temperatures is in the teens or below, Weezy shivers and doesn’t like to be on the walk longer than 10 minutes or so. He’s pretty sensitive to weather - he had a small heatstroke this past summer in 80 degree weather.