Not 100% sure about Austria but you might need special winter tyres too, at least in Germany:
Germany
Since November 2010, cars driving in wintry conditions have to be equipped with winter tires and enough screen washer liquid. This also applies to foreign cars. The fine for driving with inappropriate tires is € 40,00. In case of danger or obstruction the fine is € 80,00. In addition to a fine, driving with inappropriate tires can lead to liability.
Switzerland, Austria, France and Italy
No general laws apply, but it is recommended. In case of an accident, the use of inappropriate tires can play an important role in establishing liability and can lead to prosecution.
On mountain roads winter tires and tire chains can be mandatory. This is indicated with a road sign