The Snow Queen

This story by Danish writer Hans Christian Andersen contains elements very reminiscent of the old sagas and legends. The title character, particularly as portrayed in the 1957 Soviet animated film, shares many characteristics with the Frost Etins. Also, the heroine's name, Gerda, is a variation of Gerd. Gerda ventures to the land of the Snow Queen to free her love Kay from the queen's icy palace. In the original story, Kay has his mind enchanted by splinters from a troll's mirror. In the animated film, his heart is turned icy by splinters from the snow queen's ice mirror, and Gerda hopes to rekindle his love and warm his heart. This is something of a turnabout on the story of Frey striving and succeeding in winning the heart of Gerd, the daughter of a Frost Giant.

Here is a clip from the first cinematic adpatation of the Andersen fairy tale, Snezhnaya koroleva, produced in the USSR in 1957. Per Wikipedia,  it was "later dubbed by Universal Studios with the voices of Sandra Dee as Gerda, Tommy Kirk as Kay and introduced by Art Linkletter. In the 1990s, the film was redubbed again, this time featuring the voices of Kathleen Turner, Mickey Rooney, Kirsten Dunst and Laura San Giacomo." This clip is in the original Russian.