The name has historic reasons and it used to be that this was the tire that was used when the snow arrived. With product developments both in the design and the materials, snow tires have now transformed into winter tires, which can and should be used for the whole season of winter from then you reach freezing temperatures.
When the winter arrives, you need a tire that is designed for winter use. Winter tires have a symbol indicating that they have been officially tested and approved for use in winter conditions. Without this symbol it is not safe to drive. The rubber compound in non-winter tires will get too hard at the low temperatures and will not give you the necessary traction and you will be left without any grip. Do not attempt this. So change to snow tires before the winter arrives and stay safe!