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?
I know that German law requires tires apt for snow in winter time
Very close, but no cigar.
The original law is:
§ 2 Abs. 3a Satz 1 StVO:
Bei Glatteis, Schneeglätte, Schneematsch, Eis- oder Reifglätte darf ein Kraftfahrzeug nur mit Reifen gefahren werden, welche die in Anhang II Nummer 2.2 der Richtlinie 92/23/EWG des Rates vom 31. März 1992 über Reifen von Kraftfahrzeugen und Kraftfahrzeugan hängern und über ihre Montage (ABl. L 129 vom 14.5.1992, S. 95), die zuletzt durch die Richtlinie 2005/11/EG (ABl. L 46 vom 17.2.2005, S. 42) geändert worden ist, beschriebenen Eigenschaften erfüllen (M+S-Reifen)
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.
To be clear, the German regulation states that M+S tires must be used in "wintry conditions". All-season tires without the M+S symbol do not qualify for wintry conditions. In most cases, tires described as all-season, multi-season or "universal all-year" are appropriate for everything but wintry conditions and so technically speaking they are not "all-season" unless of course you live or drive in a climate where "wintry conditions" do not occur. Tires with the specific M+S symbol or the snowflake and mountain symbol are designed specifically for snowy and icy conditions and are quite different from other types of multi-season tires.