You may not need snow chains as you can't use them everywhere but winter tyres are a legal requirement, Vredestein Quatrac 3 would be a decent tyre to put on for all season use.
from the web
Winter tyres are mandatory in Austria. The law states that passenger cars with a permissible maximum weight of up to 3.5 tonnes may be operated only between 1 November and 15 April in winter conditions such as snow, slush or ice if winter tyres have been installed on all wheels. All-season tyres are also considered winter tyres if they have the "M + S" mark.
As an alternative to winter tyres, snow chains may be used on at least two driving wheels, however, these may only be used in case the road is covered by a complete or scarcely broken snow cover or sheet of ice. Failure to comply with the law results in a fine up to 5,000 Euros and the vehicle could be impounded. Insurance is deemed void if a vehicle which is involved in an accident between November 1 and April 15 is not fitted with winter tyres.
