Rural areas are much more common in the US than in other countries and much more likely to lose power in a storm, due to the long lengths of power line needed and the lack of redundancy from being too sparse to have multiple feed-ins to the local substation.
It's not the cold that knocks out power, it's the wet and saturated ground and high winds knocking trees into the power lines.
I live in literally the middle of nowhere and get very bad winters but I lose power less often than I ever did living in the center of Chicago which often lost power for days at a time due to the weather.