The track is open throughout the whole year. The northern loop of the Nurburgring is open to the public on some weekends and in the evenings during the year. Actual opening times vary depending on the time of year and also to fit around manufacture testing and race events.
There is a calendar which is published on the Nurburgring website that details which days it is open to the public. On the official site you will also be able to see details of any racing events taking part on either the Northern Loop or GP circuit. Click on the picture below to view the official Nurburgring calendar of events.