In the first paragraph, in the sadness of being polluted, the snow drifted and the wind blew.

It should be about what the author saw. We can guess that the author is in the snow.

In the second paragraph, I was covered in dirty sadness, like a fox fur coat, covered in dirty sadness and curled up with snowflakes.

Tell me about the author's clothes. Wearing a fur coat, I shivered in the snow.

The third paragraph, polluted sadness, does not expect anything, nor does it pray/ask.

Dirty and sad, dreaming of death in boredom.

It should be the writer's drunken life. Nothing to ask for, immersed in the fantasy of alcohol.

In the fourth paragraph, I am also afraid of being polluted by sadness and pain.

I don't quite understand this sentence. Is it "feeling painful fear"?

The sadness of being polluted is helpless, and the days pass by day.

There is a saying translated into this, personally feel that there is "much ado about nothing, ushered in the sunset." Meaning, think of the source of mulberry "そして, life わつつく" and other husbands of the deceased, day and night.

The whole poem is about sadness. Cold makes the body feel sad, and mental depression pollutes this sadness.