Curse of a Thousand Winters
About two hundred years after the events of Breath of the Wild, where the hero is long dead and his exploits the stuff of naught but legend, a sudden ice age overtook the lands that were once one unified kingdom. No one knows where the sudden snows came from or why, only that they must be cursed, as they have yet to let up even half a century later. This caused serious problems with agriculture, leading to a widespread famine across the land before the transition to root vegetables and hardier plants capable of surviving the snows was made.
The Hebra Region became nigh-uninhabitable, forcing the rito to migrate south and resettle in the areas around Hyrule Ridge. This has brought them into conflict with Hyrule Kingdom, as the hylians hardly took kindly to the rito suddenly waltzing in and taking some of their land, regardless of if they had any other choice or not. Egos were offended and war was declared, bringing both rito and hylian into a heated fight for the rights to the contested territory. Known as the War of Spears, this fight has raged on nearly as long as the cursed snows themselves, and has sowed bitter hatred between the two races.
Further south, the Gerudo Desert has abruptly found itself less of a traditional desert and more of a tundra, with the cliffsides around them becoming just as hostile to life as the Hebra region to the north, rendering their ice magic much less effective. The Gerudo turned to the Sheikah for their skill in fire magic, and the two peoples have actually flourished in a growing friendship and alliance. It's become quite a common sight to see both Sheikah and Gerudo milling around in their respective cities - though the Gerudo capital is, of course, restricted to females only. There is currently a divide among the Gerudo people on whether or not trans women "count"; currently, they're allowed in under the definition that trans woman is still woman, but there is a not-so-insubstantial group that wants to change that.
The most ironic change happens to be in the once-tropical Faron Region, which now finds itself more of a temperate forest. Warm air from the southern gulf keeps places like Lurelin village in more agreeably warm climes, while further out the tropical plants that once made up the face of the region have entirely disappeared. Understandably, bananas, coconuts, and durians have become popular exports along with the traditional seafood.
Death Mountain is, unsurprisingly, the location that was changed the least in this age of snow and ice. I mean, it's a VOLCANO. Sure, it's not hot enough to freaking set your clothes on fire, not anymore, but it's still exposed magma. It creates quite the interesting dynamic in places where the magma isn't quite so present, leading to Death Mountain's newer (but still lesser-used) nickname as the Mountain of Fire and Ice.
As for the Koroks, they're not really affected much either. Warm air from Death Mountain rushes down the sides and through the Great Forest of Hyrule, keeping the place warm enough to simply be a snow-covered forest rather than an ice cube like the rest of northern Hyrule. Diamond dust floats in the air in place of the mist that once pervaded the woods - a beautiful hazard even more deadly than it appears.
The zora of the Lanayru region were lucky. Ice has become a prevalent fixture, with several frozen waterfalls and a significant portion of their lake completely coated in it. But thanks to the scaled bodies of the zora already being adapted for the frigid waters of the mountainous region, they've stayed warm even as the land freezes around them.
And last but not least, Kakariko and Hateno villages. The Necluda region has become much the same as the Great Forest of Hyrule, covered in boreal forests almost eternally blanketed in snow. Hateno in particular has become famous for its "green longhouses", giant greenhouses capable of housing and protecting their crops from the never-ending winter. As an aside, glass-making has become a rather popular career choice among the locals.
(As for the Yiga? We don't talk about the Yiga. Not their frozen hideaways in the sheer cliffs bordering the Gerudo Desert, coated in frost and ice, body after body after body found frozen in the caverns and sand.)
(No, we don't talk about the Yiga. Not anymore.)
What could have triggered this terrible winter storm, that swept through the kingdom and never let go? What could have so angered the gods, that they would smite the lands with never-ending snow and ice a thousand times stronger than any winter? Some say the gods have cursed the land in their anger, to suffer a thousand winters before the people could feel the sweet relief of spring again. Others say this winter is of man's own making, of disturbing something they should not and dooming the land to freeze for all eternity from their own hubris.
Whether you call it the curse of a thousand winters or the curse of an eternal one matters not. The truth is, no one knows. All we know is that it came from the north; a frigid, biting wind rushing southward, bringing chilling death in its wake. And here it has stayed ever since.