In case of much snow, german airport could be closed for some hours, but this happens rarely, because the amount of snow isn´t often so high that it its necessary to close.
In Germany, the conditions of airports are different. So if there´s snow at FRA, there doesn´t need to be snow at CGN. These airports for example are only 2 hours away from each other. So if FRA has to be closed, a part of the long haul flights would get down at CGN. If the weather is better, they set over to FRA. Passengers would be transported by bus to FRA.
In Germany many international airports are close together, this helps in case of long haul flights.
With domestic flights, you have the same problem as everywhere when an airport is closed.