Idk about Germany, but this cannot happen in France, the climat is way too warm for that.

Edit: having looked a bit more in details, it looks like even though the rivers can't be frozen to a point it stops the plant from functioning, the water admission systems can (partially) freeze in extreme weather and it happened a few time in France already.

In Finland the nuclear plants are by the sea, I'd imagine this to be at least part of the reason.

Finnish plants have to reduce capacity during hot summers too, but it's because of their environmental requirements: the exhaust water back to the sea must not exceed a given threshold to protect marine life.

It's also because of environmental requirements in France, and I expect in Germany as well.

Nuclear plants could use warmer water, but regulation forbids them from releasing water at a higher temperature than 30°C.

Freezing rivers are less of a pfroblem in Germany and France, but the rivers can be low on water so that the cooling might be limited in the winter. And there have been winters, where the nuclear production in France was struggling keep up with the heating requirements.

It'd be technically interesting to see how expensive it is to mine the ice and shovel it into directly into the cooling system somehow. It isn't like there is a problem finding heat to melt the ice once it is on site, absorbing waste heat is the whole point.