Appropriate tires: It is important to make sure your vehicle is prepared for winter conditions. Article 2 of the German traffic regulations requires the use of suitable tires when road conditions are icy. Appropriate winter and all-season tires will have a marking indicating that they are rated as appropriate for driving in snowy and/or icy conditions. The marking is a snowflake (indicating tires suitable for snow).
If you are found driving in winter conditions without the appropriate tires, you could be fined €60 and given a point against your license. If you impede traffic, the fine could be €80 and a point against your license. In case you endanger someone, the penalty could be €100 and a point against your license. If you cause an accident with the wrong tires, you could pay €120 and receive a point against your license. In addition to that, if you are involved in an accident and your vehicle is equipped with the wrong tires, your car insurance may hold you completely or partially liable for the damage.
Driving in other European countries: In general, it is highly recommended to familiarize yourself with the traffic rules of the country you intend to visit. This applies even more for the winter season.
Please see the following links for further information:
https://www.german-way.com/travel-and-tourism/driving-in-europe/driving/snow-tires-winter-driving/
http://ec.europa.eu/transport/road_safety/going_abroad/index_en.htm