[Jurgis]

In Germany only the tread depth is limited by law. It has to be more than 1/16" (1.6mm).
Summer tires should be not older than 10 years, tread depth 1/16".
No information for the age of winter tires, tread depth should be more than 5/32".
Tires at trailers are limited to 6 years, tread depth 1/16".
If tires have visible damages they have to be replaced immediately.

If you have an accident and your tires are just close to that limit but still ok it may be that the insurance will not pay all because the accident might not have happened with better tires.