Hans Christian Andersen's story is simplified in this animated feature, which begins with an animated copy of his fairy tales, introduced by a little man, who says he is "old Dreamy" ("Ole Lukøje"). Old Dreamy tells the viewer that on days when the master storyteller Andersen is not overtired, he puts him to sleep with his colorful, magic umbrella ("slumbrella") that also causes him to dream wonderful stories, which he then writes as his fairy tales. Old Dreamy then narrates the story of the Snow Queen, which he begins with Kay and Gerda up in their window box garden, planting two roses together, which Kay calls "our roses",
On a winter night following, Gerda's grandmother tells the two children the legend of the Snow Queen, and while she tells it the viewer is taken to the Snow Queen's palace of ice in the far north (on Spitsbergen) where she sits on her throne and looks into her mirror. The Snow Queen's proud and frowning face is seen in Gerda's frosted window to Gerda's exclamation, "It's the Snow Queen!". Kay jokes, "Let her come in here, and I'll put her on a hot stove!". This angers the Snow Queen, who is watching the children from her mirror, which she smashes with her scepter, telling the ice splinters of the shattered mirror to go into the eyes and hearts of those who have offended her. Back at Gerda's home the window bursts open, letting in ice splinters that get into Kay's eyes and heart. His personality changes: he is hostile toward Gerda, and when Gerda notices that the letting in of the cold wind and snow has killed their roses, which have turned black, Kay stomps on them and kicks them about in glee. He then leaves Gerda in tears to be comforted by her grandmother.
When Kay goes out on the next day to ride around on his sled in the marketplace of the city, Gerda wants to come along, riding on Kay's sled as she has always done. Kay pulls the sled fast, knocking Gerda off, but she tries not to cry. Kay ties his sled to the sleigh of the Snow Queen, which has suddenly appeared, to Gerda's horror. The Snow Queen pulls Kay on his sled out of the city, where she stops and confronts him, taking him into her arms as her willing captive, since his heart is as cold as ice. The Snow Queen's presence freezes a mother bird to death as she protects her young under her. These young birds will appear later in the story.
Old Dreamy then tells about Gerda's going out to look for Kay. She asks young birds and animals to no avail if they had seen Kay. A little lamb tells her, "I don't know from nothing, I was born yesterday". At the river side Gerda begs the river to take her in a row boat to Kay. She gives her new red shoes to the river, and her boat is guided down the stream to where the home of the kind, old sorceress is. She comes out of her garden to the trumpeting and drumming of four toy soldiers, who stand at her gate as sentinels. As Gerda's boat approaches, the old woman uses her crook to pull it to shore. She takes Gerda into her garden, which is eternally in summer with flowers that sparkle. In her house the old woman puts Gerda to sleep by combing her hair. It is her intention for Gerda to stay with her and forget looking for Kay, but Gerda awakes while the old woman is still sleeping. Gerda remembers that she is looking for Kay, but when she gets to the gate she finds that outside the garden it is already fall. She begs the toy soldier sentinels not to sound their bugles and drums to awaken their mistress, and they comply.
Gerda is next found by the seashore where she is met by a raven, "Mr. Corax" (Latin for "raven"). Gerda tells him that she is looking for a "good, kind, brave boy". Mr. Corax tells her that such a boy is now living at the palace of the princess with whom he is "palsy walsy." Mr. Corax takes Gerda to the palace to find his "lady friend", a female raven, named Henrietta, who knows the palace and can guide Gerda through it. They arrive when there is a ball going on in the palace concluded with fireworks. When all are asleep the ravens take Gerda into the palace to the royal bedroom. Gerda takes a candle that she uses to see if the boy is Kay. It is a different boy, who is heavier than Kay. The shock of awaking him, awakens the princess, who calls her guards. The three intruders are apprehended, but when the princess is caught up in the romance of a girl seeking her boyfriend, she and her consort decide to help her.
An interlude follows with the Snow Queen and Kay talking in her ice palace throne room. Kay is playing with ice crystals when the Snow Queen asks him if he knows what love is. He remembers Gerda, but he stays there because his heart is a lump of ice like the Snow Queen.
The princess and her consort send Gerda on her way with a golden coach and attendants. While the coach travels through a dark woods, they are stopped by a gang of robbers, who take Gerda and strip the coach of its gold plate, sparing the attendants. An old hag takes Gerda, but when she is bitten on the ear by her daughter Angel, who is riding on her back, she listens to her request to keep Gerda with her other captive pets. These pets include a fox, little rabbits, the birds that were spared the Snow Queen's frost earlier, and a large reindeer, named Bucky Boy. The birds tell Gerda that they saw the Snow Queen take Kay with her to Lapland. The reindeer offers to take Gerda there. It remains for the robber girl to let Gerda and Bucky Boy go, which she does. She also releases the birds, the fox, and the rabbits, but they decide to stay with her.
Gerda and Bucky get to the Lapland woman, who warms them by their fire. She tells them that the Snow Queen had stopped there with Kay but went on farther north to "Finland". She directs them to her cousin in Finland who can direct them further, and she writes a letter to her on a fish that she sends with Gerda and Bucky. When Gerda and Bucky get to the cousin in Finland, she tells them that they are just 10 miles away from the Snow Queen's palace. Gerda and Bucky leave so quickly that Gerda leaves behind her mittens and cap.
Bucky, who collapses along the way, is unable to take Gerda up to the ice palace, so Gerda goes on alone. When Gerda finally gets to the palace through the blustery wind and snow, she encounters Kay, who is released from the splinters of ice in his eye and his heart by Gerda's warm embrace. Even though the Snow Queen suddenly returns, she and her palace melt away with the coming of spring.
Gerda and Kay are taken first by Bucky Boy to the Finnish woman, who takes them further on their journey home in her dog sled. The Lapland woman takes them further in her boat, and the robber girl takes them the rest of the way in the coach that had been stripped of its gold plate. They go past the princess, her consort, and the ravens who wave them on. They are now home again in their window box garden in springtime. Old Dreamy tells the viewer that later Gerda and Kay were married, but "that", he says, "is another story".
In 1959, the film was dubbed into English and released by Universal Pictures with the voices of Sandra Dee and Tommy Kirk as Gerda and Kay. This version is introduced by a six-minute live-action Christmas prologue featuring TV personality Art Linkletter, as well as a two-minute montage. In this prologue, Linkletter recited the following rhyme just before the film began: "One snowflake two/three snowflakes four/And now you'll see 'The Snow Queen'/if you add a million more." The American version also contained an entirely rewritten musical score and had three new songs in English, two of which replaced the Russian songs (the other one was in the montage).
In the 1990s Films by Jove restored the film and created a new English soundtrack for it, featuring the voices of Kathleen Turner, Mickey Rooney, Kirsten Dunst and Laura San Giacomo. It was shown on television in 1998 as part of the "Mikhail Baryshnikov's Stories from My Childhood" series, and was later released on video and DVD in 1999. French and Spanish soundtracks were added for the DVD version, the French soundtrack featuring Catherine Deneuve, and the Spanish track Beatriz Aguirre. Following criticism of the non-inclusion of the Russian soundtrack on the DVD, Films by Jove also released a DVD of the film containing the original Russian soundtrack with English subtitles sometime in 2006.