In January, dog ownership can get complicated. Some pups love the snow, ice, sleet & hail. Lots of pups are more sensible though, and hate it; so how in the world do you get the haters to do their business outside? Even dogs like Huskeys and Malamutes who are bred for snow will sometimes gleefully run through snow piles outdoors, then come into your living room to pee!
First of all, dogs with thin coats need to be covered when it's below freezing, even if they're only out for a brief time. Boxers, Great Danes, Bulldogs, Chihuahuas, Dobermans, Pointers... all the pups with little to no insulation need a warm coat and possibly foot coverings that are made for dogs. Check petedge.com for coats and boots. If you send these dogs out uncovered, the risk is that after a few moments, all they'll think about is how to get back inside. Where they will procede to dump in your study or pee on baby's highchair.
The next problem is where do they go? If you're like most households, snow shoveling and snow blowing have made Fluffy's favorite spot inaccessible. Most likely, she will try to get to her usual place while looking back at you in great perplexity. Little dogs often stare at piles of snow and give up entirely. So it's advisable to keep an outdoor space clear for your dog(s) in the winter. If someone plows your driveway, you can walk the dogs there, giving them a treat when they relieve themselves, so they'll know that the driveway's ok in the winter. Don't worry about poops in your June driveway - dogs prefer dirt, garden, or lawn if they can get to it.
If there's no driveway option, clear a space on your property. I make a circle about 15 feet in diameter just to the side of the porch steps, because like many canines, Benny and Daphne wander in circles when they need to poop. Daphne even does it before she pees. You need a long-handled pooper-scooper set-up so you can clean up after they do their deed, whether they chose your cleared area or the side of a snowpile. It is rare that nature presents a more revolting spectable than a springtime dogpatch that has not been kept clean. I keep a small covered bucket with a trash bag liner in the cleared area. I clean up pee spots too, 'cause I don't want my lawn to go into shock when the snow melts. Once a week the poopy bucket liner goes out with the trash.
If they're having a good time outside, dogs love to eat snow. Not a great idea. We get lots of intestinal infections in Doggie Den Day Care with dogs who have eaten unclean snow. Even in a pristine area, they like to lick snow where other mysterious beings have trod, and moose pee is not necessarily a good nutrient. So have a good time, keep her warm, limit the snow intake, and keep one area clean and clear for when she needs to get serious.