This is the 544th most frequent Polish word.
śniegu
"Śniegu" means "of snow" (genitive singular form of "śnieg").
In this sentence, 'śniegu' is in the genitive singular form, used here to express quantity (a lot of something).
W tym roku spadło dużo śniegu.
This year, a lot of snow has fallen.
Here, 'śniegu' is again in the genitive singular form, utilized to indicate the presence of some amount of snow.
Na szczycie góry wciąż jest trochę śniegu.
There is still some snow on the mountain peak.
In this third sentence, 'śniegu' continues to appear in the genitive singular form, denoting the cause of the slipperiness.