I know that German law requires tires apt for snow in winter time. It's quite obvious that I cannot use summer tires, but can I go on universal all-year tires?
What are the exact requirements?
Very close, but no cigar.
The original law is:
Translation: "If (all possible combinations of slippery conditions) happens, a car may only be driven with (blah) M+S tires".
It means that as long as the weather and the streets are fine, you may use summer tires, there is no time limit. But as noone can predict for sure when snow or black ice is coming, it is recommend that you use winter tires from October to April.
EDIT: For the second question: Yes, you can use all-year tires.
Yes you can. If there is no snow/ice you are allowed to drive with summer tires, but it's not a good idea. But if your tires have M+S symbol it's allowed to drive with them in winter (in summer too)
Here is a link to the source (only in German)