A man who was supposed to be picked up and taken somewhere safe from the encroaching ice has been left behind. At the end he hears the book and crackle of the approaching mass of ice. (It's a metaphor, I know). I'd like to find it again. I read it a long time ago, so it isn't new.
This struck such a note of recognition in my head that I had to look for it. I think this is The Forgotten Enemy by Arthur C. Clarke. The story originally appeared in New Worlds magazine in 1949 so it is quite old.
This classic story has a man who stays behind in London to stay with his books when all others leave the city, as the earth has entered a belt of dust and the strength of the sun is diminished. So Britain cools down and people leave for warmer places.
He encounters polar bears, reindeer and wolves, and hears a "roaring" sound.
At first he thinks it may be a rescue party but it turns out to be
the noise made by advancing glaciers as they cover Britain again