Act I
A Greek chorus introduces Princess Elsa of Arendelle and her playful younger sister, Princess Anna ("Vuelie", "Let the Sun Shine On").[31] While the family knows about Elsa's magic, it is kept a secret from the people of Arendelle. One night at bedtime, Elsa and Anna build a magical snowman and name it Olaf ("A Little Bit of You"); Elsa creates snow in their room. In their excitement, Elsa accidentally injures Anna with her icy magic. Their parents, King Agnarr and Queen Iduna, call for the aid of the colony of hidden folk, led by Grand Pabbie. He heals Anna and removes her memories of Elsa's magic. Elsa asks Grand Pabbie to remove her magic, but he says that it is a part of her. He gives her a vision of her future, frightening Elsa, who believes that her magic will cause death. The King isolates the sisters within the castle. Elsa shuts Anna out when Anna seeks to play ("Do You Want to Build a Snowman?"), and Elsa's fear of her powers grows. While the princesses are still young, the Queen and King sail to seek a solution to help Elsa control her powers, and they die at sea during a storm.

Years pass. The day before Elsa's coronation as Queen of Arendelle, Anna asks if there is anything she can do for her sister. Elsa, her room coated in ice, refuses to open her door out of fear of hurting Anna again. Anna is excited for the castle's gates to open ("For the First Time in Forever") and meets the handsome Prince Hans ("Hans of the Southern Isles"). Elsa is terrified that the kingdom's citizens might find out about her powers and fear her, while wishing to be able to reconnect with Anna ("Dangerous to Dream"). Elsa's coronation goes smoothly, and she initiates her first contact with Anna in years. They enjoy the coronation together, with Anna talking the Duke of Weselton out of dancing with the newly crowned Queen. However, Elsa leaves after Anna asks about keeping the gates open. Anna falls in love with Hans ("Love Is an Open Door"), who quickly proposes marriage to her, and the two share a kiss after she accepts. The couple asks for Elsa's blessing, who objects because the two have only known each other for a day. After intense questioning from Anna about shutting her out of her life, Elsa accidentally unleashes her powers before the court. The Duke brands her a monster. Elsa flees to the North Mountain without realizing that her suppressed magic has engulfed Arendelle in an eternal winter.

Anna goes in search of Elsa, leaving Hans in charge of the kingdom during her absence. Up in the mountains, ice harvester Kristoff and his reindeer Sven ("Reindeer(s) Are Better Than People") are found by the ill-equipped Anna, still in her coronation dress. She orders Kristoff to take her to the North Mountain, the source of the storm. Kristoff gives her a set of winter clothes, and she leaves her dress behind. In view of her sudden engagement, Kristoff and Anna disagree about love as they cross a bridge ("What Do You Know About Love"), and Anna saves Kristoff from falling off the bridge. Anna and Kristoff then encounter a newly created Olaf, who offers to guide them to Elsa and sings about his love for summer ("In Summer"). A soldier arrives in Arendelle with Anna's dress, and Hans fears for Anna's safety. He assembles a search party ("Hans of the Southern Isles" (reprise)), including the Duke and two of his men, who intend to put her in her place. Meanwhile, on the North Mountain, Elsa builds an ice castle with her powers and transforms her coronation dress into a sparkly ice gown ("Let It Go").

Act II
Anna, Kristoff, and Olaf arrive at Wandering Oaken's Trading Post & Sauna to meet the owner, Oaken ("Hygge"). Anna enjoys the sauna together with its many other patrons. Kristoff convinces Oaken and his patrons to aid their journey; Oaken gives them provisions and a winter dress for Anna.

Reaching the ice palace, Anna meets Elsa, but when she reveals what has become of Arendelle, Elsa becomes angry and frustrated, saying that she cannot fix it, and she accidentally freezes Anna's heart ("I Can't Lose You"). Out of fear of hurting Anna further, Elsa forces her, Kristoff, Sven, and Olaf out of the palace. Anna's hair begins turning white, so Kristoff takes her to meet the hidden folk, his adoptive family, who recognize Anna as the princess and attempt to match her with Kristoff, despite him mentioning her betrothal to Hans ("Fixer Upper"). Grand Pabbie attempts to remove the magic freezing Anna's heart but fails; Kristoff realizes that he is falling in love with her ("Kristoff Lullaby"). Grand Pabbie reveals that Anna will freeze solid unless "an act of true love" reverses the spell. Kristoff selflessly races Anna back home so Hans can give her true love's kiss.

In the ice castle, Elsa considers whether she is a monster and wonders how can she end the storm, unsure whether the storm would end or grow worse if she were to die ("Monster"). She resolves to stay alive to end the storm and lowers the defenses around the castle, allowing Hans and his men to capture her. Home, Anna is delivered to Hans, but rather than kissing her, he reveals that he has been plotting to seize the throne of Arendelle by allowing Anna to freeze to death and accusing Elsa of her murder ("Hans of the Southern Isles" (reprise 2)). Hans locks Anna in a room to die, as Anna reflects on her mistakes while still holding on to the idea of love ("True Love"). Olaf frees Anna, and they venture into the blizzard outside to meet Kristoff, whom Olaf reveals is in love with her.

Hans publicly charges Elsa with treason and sentences her to death. Elsa escapes her chains and flees outside as a blizzard grows ("Colder by the Minute"). Kristoff and Anna struggle to find each other. Hans confronts Elsa, claiming that she killed Anna, causing Elsa to break down and the storm to pause. Anna finally finds Kristoff but spots Hans about to kill Elsa; she leaps in the way and freezes solid, stopping Hans. Devastated, Elsa mourns her sister, who thaws out, her sacrifice constituting "an act of true love". Realizing that her magic is controlled by love, Elsa ends the winter ("Vuelie (Love Thaws)"). Anna punches Hans, and she and Kristoff become a couple. Elsa and Anna reunite without fear for the first time, as their parents, young Elsa and young Anna appear in the background, signaling the healing of the sisters' painful past (Finale).