This is the 17982nd most frequent Polish word.
śnieżnej
"Śnieżnej" means "snowy" (genitive or dative singular feminine form).
The word 'śnieżnej' here is the genitive singular form of the adjective 'śnieżny,' describing the mountain with a characteristic relating to snow, specifically a snowy mountain.
Zimą na szlakach śnieżnej góry jest bardzo pięknie.
In winter, the trails on the snowy mountain are very beautiful.
In this sentence, 'śnieżnej' describes the color characteristic of the eagle's plumage, indicating white or snowy.
Spotkaliśmy tam orła śnieżnej kolorystyki.
We met an eagle there with snowy coloring.
Here, 'śnieżnej' is used to describe the storm, indicating its association with or characteristic involving snow.