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How is she (Demeter) related to winter?
Hades had control over her daughter, Persephone, this made her angry. Demeter laid a curse upon the earth, this frightened Hades and he agreed to let Persephone go, but since he had control over her, she had to go live with him in the underworld four out of the twelve months. During this time Demeter would be sad thus she created winter during those four months without her daughter (after the four mother when Persephone was let back to her mother, Demeter would make it spring)