Ice by Anna Kavan

The world is threatened by encroaching ice, creeping down day by day from the polar ice caps. The imminent catastrophe has thrown the world's governments into chaos, and no one knows whether the disaster has an environmental or nuclear cause, or how soon the end will come. One man pursues his sylph-like, silver-haired ex-fiancée ('the girl') as she flees from country to country, away from her husband; away from the malevolent 'warden' of one of the proto-territories that have sprung up as traditional societies crumble; away from him.