In Game of Thrones, several dialogues mention the lengthy winters and the fears they impose on people. We know that the weather system in Westeros is quite different from our world, and each season may last for ages. From the beginning of the first season, the Starks' motto was winter is coming, which made the impression that a long and cold winter will be inevitable. This article says
In the Song of Ice and Fire books, lengthy winters are feared in part for their association with supernatural threats. According to Westerosi legend, the white walkers first appeared 8,000 years before the events of Game of Thrones, during the Long Night—an icy season so severe it shut out daylight and stretched on for a generation. That’s cool. But unpredictable weather is more interesting as a factor for what it can illustrate about the characters we’re already invested in, and how it might affect the melee for the crown.
And I vaguely remember that somewhere in the show someone said there has been a long time since the last winter, so the upcoming winter is likely to be very long and hard (I don't remember which episode exactly). In the final episodes of season 7, we saw that the winter has officially come. But in season 8, especially after the third episode, it seems that winter is no longer mentioned or feared anymore.
So what happened to the long-expected winter? Did it simply pass after the death of the night king?
“Oh, my sweet summer child," Old Nan said quietly, "what do you know of fear? Fear is for the winter, my little lord, when the snows fall a hundred feet deep and the ice wind comes howling out of the north. Fear is for the long night, when the sun hides its face for years at a time, and little children are born and live and die all in darkness while the direwolves grow gaunt and hungry, and the white walkers move through the woods”
George R.R. Martin, A Game of Thrones