Car races

You probably won't find any races that late with the cold weather and driver safety. The international Formula 1 races are in Brazil and Abu Dahbi in late November. Not near the european tracks. The GT4's stop in October in Europe. You can find more of the different circuts and race types here. It says 2013 in the link but the dates are 2016 when you go to it. Only thing in December is in Valencia Spain.

https://sportscarracingnews.com/2013-calendar/

Makes sense. Thanks!!!

Your kids might like Hangar 7 in Salzburg which is a day trip from Munich:

https://en.m.wikipedia.org/wiki/Hangar-7

It's not a "race," but for a different kind of car excitement, be sure to go up the Arc de Triomphe in Paris. The view of the driving around the Arc from up top is endlessly entertaining (it's like ballet, but with cars instead of dancers, watching them weave in and out of the multiple lanes as they go round and round).

As Robert says November and December is actually in the off-season for racing. In Kerpen near Cologne you have the Michael Schumacher Kart and Event Centre http://www.ms-kartcenter.de/en/home.html and more south of Cologne also that famous Nürburgring http://www.nuerburgring.de/en/home.html

Usually every year the Race of Champions takes place in this period, but not certain where and when this year. http://www.raceofchampions.com/

As said, everything is finished by then. Even the DTM.