For Germany ignore advice written in #1. Also in lower northern parts of Germany we had sometimes winter conditions in April. Just check climate tables.
"When roads are slippery due to freezing rain, packed snow, slush, black ice or hoar frost, a motor vehicle may not be operated unless it is fitted with tyres that have the characteristics described in ... (winter tyres)"
Official German Road Traffic Regulations in German.
Rule of thumb. If you expect temperatures lower than 5 - 7 C your car shall have winter tyres.
In my opinion just book them and check if they have a M+S signature on the side. In case of accident you will lose parts of liability without the right tyres under needed conditions.
At this occasion: Make sure that you have valid driving permission with you, this can differ from having a driver's license only. This is not for rental car company but for official checks. In Germany it means this: https://www.bmvi.de/SharedDocs/EN/Articles/StV/validity-foreign-driving-licences-in-germany.html?nn=187598
For other countries better ask different forum.