This isn't a general-winter-weather thing like that. The polar vortex is a very particular phenomena that only lasts 1-3 days* and doesn't necessarily come with snow. Its signature is just extreme cold, on the order of -40 degrees or lower, even in areas that only very rarely go below -5 F (-20 C).

* technically it's always there around the north pole, but we only talk about it when it dips down into populated areas.