Wolpertingers are Germany’s answer to the jackalope. In fact, the jackalope may have come from the German wolpertinger legend.
Wolpertiners are generally rabbits or hares with horns and/or wings.
The Shope papilloma virus causes cottontail rabbits to develop horn-like tumors, so it may be based on something in reality. However, cottontails are found only in the New World, so it may not be based upon these real life horned rabbits. I don’t know if the virus has been documented in Old World hares or rabbits or if another condition causes horn-like growths in these rabbits and hares.
As for the wings, well, I happened to come across a large display of wolpertingers as the German Hunting and Fishing Museum. One display showed very clearly how the wings were inherited.
Yes, by rabbits mating with chickens.
How else do you think they’d be inherited?