Demeter is the Greek goddess of grain, and her daughter Persephone is Spring personified. Persephone's husband is Hades, god of the underworld, and she is compelled to spend part of each year with him. The time she spends with him is winter.
In Orphic theology, Demeter is the mother of Zeus, and her daughter Persephone is, by Zeus, the mother of Dionysos. The rest of the Greeks knew Demeter as the sister of Zeus, mother of Persephone by Zeus, and one of the twelve greatest Olympian gods. Demeter is goddess of grain, cultivation and the harvest. She also gave humanity the Elusinian Mysteries.
The most famous and important myth about Demeter is the story of how she lost her daughter Persephone to Hades, god of the underworld and lord of the dead. It is told in one of the oldest Homeric Hymns.
When Persephone was playing apart from her mother one day, gathering flowers with nymphs and naiads of the ocean, she spied a particularly beautiful flower, the narcissus. She went to take it, and the earth gaped open. Hades, lord of the underworld and of the dead, came forth in a chariot to carry her away.
Demeter searched for her daughter for nine days, refusing all food. On the tenth she learned from Helios the sun that her daughter was beneath the earth, with death. Helios also told her that Zeus had given his consent to Hades.
Demeter continued to wander the earth and mourn. Eventually she came to Elusis, disguised as an old woman, where a rich family offered her shelter in return for nursing their son. She consented, and the son grew like a god. She attempted to make the son immortal by burning away his mortal part in a fire, but was seen by his mother, who was understandably frightened, and screamed. Demeter became angry, revealed herself as a goddess, and told the family that her plan to make the child immortal had been ruined. She then commanded that the people of Elusis build her a temple and hold rites there in her honour, to regain her favour.
Winter and Spring
After the temple was built, Demeter sat in it and mourned. As she did so, a terrible winter fell on the earth, and there was mass famine. Zeus sent messengers to her imploring her to let her grains and fruits grow again, but she refused to do so until her daughter was returned. Eventually, Zeus gave in, and ordered Hades to let Persephone go.
Hades relenquished her, but not before persuading Persephone to eat a pomegranate seed. And because she had tasted food in the underworld, Hades retained a claim on her, and she was made to return to him for a part of each year. When she leaves, Demeter sorrows, and we have winter.