Now I come across another [online] source
that says that "Schneewurz" means
Sedum telephium, which is something else again.

But Sedum telephium's description (in my native English)
corresponds nicely with the description in the poem:
winter cold does not bother it,
and it can grow in the shade.

Leeneia,
the beginning of the poem is a description of
the forest in the grip of a bitter winter,
freezing the streams,
killing off young growing plants,
while the Schneewurz pushes itself through the cold earth
and sings its own homely little song.
While the "frozen" birds are singing
"O, woe, the sun is dead!"