All-season tires are a compromise intended to provide acceptable characteristics under a wide variety of conditions. That compromise hinders the tires from being a master of any of of them. A tire's tread design and compounds that provide extended mileage and durability under the summer's sun are not as effective in winter's freezing temperatures and through snow or on ice.
While one tire can't be the fastest on the track and most controllable in the snow, winter / snow tires are designed to excel in colder temperatures, slush, snow and on ice. So instead of white knuckling it through the three-plus months of winter, invest in winter wheels and tires to make the winter driving months as safe as possible.
Watch "All-Season vs. Winter / Snow Tires" to see the difference in acceleration, stopping and cornering capabilities between the two types of tires.