Apart from Austria, the following countries require winter tyres to be fitted, usually from the 1st November until the 1st or the 15th March:
Estonia
Finland
France (locally on some mountain passes, only where signposted)
Germany (winter tyres are not explictly required, but tyre equipment must be 'appropriate for the conditions'. This, basically, makes them mandatory)
Lithuania
Latvia
Norway (same as in Germany, winter tyres are not explictly required, but the law states that the tyres must have 'adequate grip'.)
Sweden
Switzerland (here again, winter tyres are not explictly required but failure to fit them will result in partial blame in case of an accident. In addition, snowchains may also be required locally on some mountain passes, as signposted)