are snow tires better than all-weather tires?
For bad winter roads the answer is a definite “yes”.
So called “all-season” tires are inherently a compromise in all seasons. If you want maximum safety during the winter, you should get a set of 4 winter tires (on their own rims)–assuming that you live in an area that warrants purchasing these tires. I strongly recommend the Michelin X-Ice tire.