In North America there is not much regulations regarding the use of winter tires, which is a bit strange, as their safety is undisputed during winter conditions. In many European countries there are quite strict regulations for winter tire use.
If you don’t have tires designed for winter use and you have extreme winter weather, you should definitely avoid driving because low temperatures will turn your tires hard and you will loose the traction that you would expect from your tires. To stay safe on the snowy, slushy and icy roads during winter you need to make sure that you put proper tires on your car. You wouldn’t imagine going out with summer shoes when it is snowing. So make sure you don’t drive with summer tires.