(sorry for answering so late, Anon! I wanted to relate the whole story, but my English isn’t as fluent as I wish it was)
And basically: yes. This story is told in Hesiod’s Theogony and in the Homeric Hymn to Demeter, which is the oldest homeric hymn known. Nowadays, mythologians also think that this is a later version of an original myth where Persephone was the Underworld queen and Hades her consort, to the contrary of the version we know, where she is the paredra. The Sumerian equivalent of this myth (Ereshkigal, Dumuzi and Inanna) follow this pattern.
According to Hesiod and Homer, Hades asked to Zeus, Persephone’s father, to abduct her and take her to his realm, since her mother Demeter wouldn’t allow her to go to the Underworld. At this time, no one ever return from here. So he abducted her while she was picking flowers in a field with the Oceanid maidens, Artemis and Athena.
Her mother searched her all other the world, grieving, when she discovered that her beloved daughter was gone. In her despair, she neglected the harvests (she’s the goddess of earth, corn and fertility), so humans began to starve. Finally, Helios told her who had taken Persephone, so she asked to Zeus a trial and/or her girl being sent back to her.
But Persephone had eaten seven pomegranate seeds, and no one can come back to the surface after having eaten Underworld food. (I think it’s a proof that she was willing to stay, because greek gods don’t need to eat. In the Iliad, it is clearly said that “the gods do not eat bread nor drink wine, hence they have no blood such as ours, and are immortal” (The Iliad, scroll V).
In the end, Persephone spend half the year with her husband, in the Underworld, and this provokes winter because her mother misses her ; and the other half of the year to the surface, in spring and summer (Ovid says half the year, but Persephone’s time with Hades can be of various lenghts, according to the author).
It’s how the ancient Greeks explained the seasons.