You vowed to love them and protect them. They are your fur-babies and are suppose to be a part of your family. If you wouldn't leave your child outside in the cold to fend for themselves or you wouldn't want to be left out in the cold and/or inclement weather, then you shouldn't be leaving your pet outside either. In fact, under Libre's Law, a dog cannot be left leashed for longer than 30 minutes in cold weather temperatures below 32 degrees Fahrenheit. This act establishes under what extreme weather conditions that keeping animals outside would constitute cruelty to animals.
Just like people, a pets cold tolerance can vary from pet to pet and these variances are in fact based on several factors including but not limited to: how their body stores fat, their coats, activity levels and their overall health. Elderly pets are at higher risk of getting cold faster. Even if you have shelter, like a dog house for your pet, this is not adequate enough in extreme cold temperatures and/or harsh snow storms. Keep in mind that dogs can suffer from hypothermia and frostbite and how quickly depends on its cold tolerance. In most cases, it is recommended that pets are not left outside in extreme temperatures for more than 30 to 45 minutes at a time.
Always keep in mind that if it is too cold for you, it is too cold for your dog or cat. Even if your cat or dog is generally an outside pet, in extreme cold or inclement weather like snow and blizzards, they will learn to be happy inside until the weather breaks. If you are worried about house training issues you can purchase a baby gate or animal carriers/kennels and leave them inside a designated area or crate when you have to leave your home. You can also keep them at bay during your sleeping hours in this capacity. For dogs who are not house broken you can lay down dog training pads in the designated area you are keeping your pet. A small litter box for your kitty will do the job, they learn fast.
There are a number of things that you can do to protect your home and floors all while protecting your animals. It is worth it. They depend on you.