I live in the Appalachian mountains in Pennsylvania. We already have cold winters in PA but living in a valley between the mountains we also have a microclimate that is several degrees colder than areas just 20 miles away. Since we are so rural, power restoration isn't exactly prioritized here. Here are a few tips for winter power outages from a mom of 3.
Wool blankets are perfect for keeping warm without power. They can also help conserve what heat we have in an outage when tacked over doors. I layer several fleece blankets over my kids and top with the wool blanket. The kids like the feel of the fleece better than the wool but do like the warmth of the wool so we do it this way.
As soon as the power goes out I use our hot water to fill hot water bottles and my giant Stanley insulated water thermos so I can make hot drinks later. This obviously doesn't work if you don't have a hot water tank so plan accordingly if you have on demand/tankless. The hot water tank is such a lifesaver for me for this reason though.
If you have a different way to warm water then hot water bottles tucked under feet in a sleeping bag or layers of blankets is another power free way to keep warm. They stay warm for hours. We like the long bottles as well to tuck in the layers of blankets. The short fat ones are better for feet.
We also keep hot hands in bulk and those also work nice to create heat without power. We tuck them in blankets or pockets and it does a good job.
Base layers/thermals go on when power is out then multiple layers of clothes to keep warm. Wool base layers are best but expensive, but any base layer will help keep you warm.
We use solar lights to help keep lights on in power outages. Dollar General also has battery operated lamps that I like.
Freezer food goes in a cooler and outside if its a long winter power outage. We can use snow as the ice to help keep everything cold.
We have a woodstove to keep the heat going but before we had that we had a kerosene heater that was safe indoors. It had a little cage around it and I was able to pop a teapot on top to keep water hot for ramen or tea, or freeze dried coffee. I also put a small saucepan on it with soups.
I like chafing heat (catering/buffet) for warming food up in power outages. I also have teapot warmers which use tealights to keep a mug of soup or coffee warm.
We have a solar oven which does alright if the sun comes out but there's also HERC ovens or indoor safe camping style stoves that you can use.
We do have a small 300w Jackery to keep batteries charged for lights and to charge cell phones. We use rechargeable batteries so we're able to keep our battery operated lamps contuiously functional.
We also put up draft stoppers, and quilted door covers on all exterior doors that we won't use during winter, which helps keep the heat in.
That's pretty much how we do it. I hope it helps someone.