I'm going to rent a car in Frankfurt, Germany in December-January. Can I assume that any car is to be equipped with winter tyres? (Reason I'm asking is that some web sites clearly state that winter tyres included, while others don't mention that at all)
Appropriate tires for driving in winter conditions (snow, slush, ice, frost) can be dedicated winter tires but there are also all-year tires that fulfil the respective regulation.
A rental car with winter tires not explicitly mentioned in January in Frankfurt may have all-year tires, but my guess is that it will anyways have winter tires as all-year tires are probably more expensive for the rental (cost more and don't last as long).
Unless you rent the car in order to go into the mountains/winter sports regions, you should be fine with winter-suitable all-year tires as well. In particular, the Rhein-Main area isn't prone to get deep snow (and if that happens, there's Chaos in captial letters) and snow usually turns into rain within hours. The bigger difficulty is that we're somewhat prone to get freezing rain (Blitzeis literally "flash ice" in German) when after a cold spell the wind changes and it rains on frozen ground. But that's outside the limits of winter tires as well...
BTW: The rental (vehicle owner) has a direct legal responsibility for having suitable tires on the car (i.e. if the car is on summer tires, they must make sure it's not driven in winter conditions - which means to not rent it out in December/January).
The driver has to make sure, too, of course.
As winter tires are legally required (for your rental time), the car rental agency must have them available on their cars - they cannot rent you a car that is not allowed on public streets.
That doesn't mean they have to give them to you for free - and some of them do charge an extra fee for winter tires; could be per day or per rental. You should clarify the potential additional cost before commiting to rent from any agency.