Starting November 1st winter tires are mandatory in Austria (until April 15th), Finland, Germany (until March 31st), and Sweden. Also, in Italy, Norway and Switzerland it is advisable to adjust your tires to the road conditions during winter months. These requirements are subject to change, so check with the countries you are visiting.
As the owner of the vehicle, it is your responsibility to 1) exercise proper judgment as far as whether local driving conditions may warrant a tire change or the usage of additional equipment such as tire socks, chains or others. 2) comply with any local regulation which may require a specific type of tires either during a certain period of the year or as a result of particular conditions.