King Agnarr

King Agnarr and Queen Iduna are minor characters in the 2013 Disney animated feature film, Frozen. They are the parents of Elsa and Anna and were the rulers of Arendelle until their deaths.

Background
King Agnarr and Queen Iduna were the rulers of Arendelle. Together, they had two fair daughters, Elsa and Anna. Although Anna was a normal child, Elsa was born with powers of ice and snow. Apparently, the parents are as powerless as Anna, but it can be presumed that either magical abilities run in the family and merely skipped their generation.

Judging by how he presents himself, Agnarr is learned, kind, powerful and diligent. Iduna appears to be far more passive, gentle, and openly emotional than her husband, though with the crucial motherly nature needed to raise Anna and Elsa. Their personalities are further explored in the novel A Frozen Heart, where several traits are revealed, including the fact that Agnarr has the tendency to spoil his daughters, and has a difficult time legitimately punishing them when they misbehave. Additionally, although Agnarr is generally docile, when on the verge of losing his temper, it is Iduna who has the ability to calm his nerves. This peacekeeping aura of the queen is also carried over to other occasions, such as Elsa's training to control her powers; the queen being far more patient and accepting of momentary breaks, in hopes of preventing Elsa from becoming overwhelmed.

With that, it was clear that the rulers' primary concern lie within their daughters, willing to make large sacrifices to ensure their safety due to Elsa's unique abilities. And despite Elsa's powers, they don't fear her in the least, giving her just as much affection as Anna, and are even willing to make physical contact with her, but eventually decided against doing so, as Elsa prefers it that way, fearful that she might hurt them.

In spite of Elsa's crippling fear of harming her parents, neither Agnarr or Iduna have ever showed fear of their daughter—only sympathy, and the fear of the hardships that may befall her should her abilities remain untamed. In fact, they appeared rather optimistic that she would one day learn to control her abilities with ease, with Agnarr noting the drastic isolation was meant to last for a temporary amount of time, until that day eventually arrived. By the time of their two-week voyage, they were so confident in their eldest daughter, that they had even planned to end the isolation, once they returned.

Names
Their names are not in the film's credits, but are seen written in the Runic alphabet on their memorial stone markers. According to those, the name of the king is Agðar (English: Agdar/Agnarr) and the name of the queen is Iðunn (English: Idun/Iduna). However, this has not been confirmed by the filmmakers.

In the books Frozen: 5-Minute Frozen Stories and A Frozen Heart, their official names are roughly the same as the translation, though slightly anglicized as Agnarr and Iduna.
 * The Queen's Name: Iðunn can be anglicized as Ithunn, or Idunn/Idun. Iðunn means 'youthful', 'eternal youth' 'again to love'. The name Idun is a popular name in Scandinavia, the setting of Frozen. The name Idun also means 'rejuvenation'.
 * The King's Name: Agðar can be anglicized as Agdar. Agðar is a male form of Agða, a short form of Agatha, meaning 'good, honorable.' Agdar is a popular name in Norway. The name Agdar means 'brave warrior' in Norse and from Greek agathos meaning 'good'.
 * Due to the Runic alphabet, the king's name can also be read as Akðar or Akthar. Some believe it could be the name Akhtar, which means 'star' and 'good luck'. The latter name is found in India, Pakistan and Bangladesh as well as Iran as a surname thus making it unlikely to be the given name of a Nordic King.

Frozen
The couple first appear after being frantically called by Elsa, who accidentally struck Anna with ice magic while playing inside the castle. They are worried about Elsa's powers getting too strong, but fortunately, they find a map in the royal library that will take them to some trolls who can help Anna.

Anna, Elsa, Agnarr and Iduna travel to the valley, where the king of the trolls, Grand Pabbie, informs them that Anna can be healed, though they're lucky she wasn't hit in the heart, for it can be fatal. Pabbie then informs the royal family that, while Elsa's magic is beautiful, she should learn to control it and not let fear consume her or else horrible things will occur. Agnarr assures that they'll help Elsa learn to conceal her powers until they can help her gain control of them. Before they depart, Pabbie wipes Anna's memories of Elsa's abilities, believing that it's best if she completely forgot about the mystical moments they shared, though rearranging the memories to make it seem as if they were playing outside in the regular snow, instead of snow conjured up in the castle.

The two sisters grow up separately to further safety upon Anna as well as keeping the castle gates closed for the kingdom's safety as well and vice-versa for Elsa (as they took Pabbie's saying "fear will be your enemy" literally). As Elsa grows, her parents try to help her control her magic ice powers. Agnarr tells Elsa "Conceal it, don't feel it, don't let it show" as a way to control her powers and to wear gloves to avoid conjuring the magic. It doesn't work completely, because Elsa can still freeze things without trying.

One day, Agnarr and Iduna are to set off on a two-week sea voyage. During a storm, they drown at sea by monstrous waves. Anna and all the people of Arendelle mourn their deaths (a portrait of the couple is draped over with a black sheet of fabric), but Elsa doesn't attend the funeral out of fear of her powers being revealed and someone getting hurt as a result, even though as the eldest sister, she's the heir to the throne. Due to their deaths, Elsa's training of her powers was left incomplete, as her powers were still mostly out of her control.

Agnarr still appears later in the film; in a painting of his own coronation seen hanging in the library of the castle when Elsa was trying to control her powers, and again when the evil Prince Hans betrays Anna in order to take over the kingdom. They are also mentioned when Kristoff asks Anna during their argument over Anna getting engaged to Hans after just meeting him, "Didn't your parents ever warn you about strangers?" to which Anna replies (rather uncomfortably), "Yes, they did." while slowly moving away from him.

Once Upon a Time
Anna and Elsa's parents appear in live-action form in the fourth season of Once Upon a Time, which the backstory of the events happening in Arendelle prior to Frozen. Although Anna and Elsa's mother was identified as Iduna based on translation of the Runic inscriptions on her tombstone in Frozen, here, she is called Gerda (A character named "Gerda" does appear in Frozen, but she is one of the servants, not the queen that preceded Elsa). She is portrayed by Pascale Hutton as an adult and by Ava Marie Telek as a child.

Gerda is the youngest child of her royal Arendelle family, and has two elder sisters, Ingrid and Helga. Ingrid, like Elsa, has the power of ice and snow.

Ingrid fears hurting her sisters with her powers, but her sisters promise to help conceal the powers, and continue to sustain their unity. Years later, on the night of their father's birthday celebration, Gerda and Helga attempt to convince Ingrid into coming with them, but her fear of ruining the party overshadows her sisters' pleads. At the party, Helga introduces a new admirer, the Duke of Weselton, to their father.

After the party, the sisters arrive home to find Ingrid packing up as she believes with herself gone, they can have normal lives, fearing she won't be able to control her powers. Gerda mentions Rumplestiltskin, who may help. In exchange for their ribbons (which the sisters used to symbolize their sisterhood), Rumplestiltskin gives Ingrid a pair of gloves to conceal her powers, as well as a urn to entrap her if she becomes too dangerous. Later, in the royal garden, Gerda comes across Ingrid crying over the frozen and crumbled body of Helga. Realizing Ingrid, whether intentionally or not, killed Helga, Gerda entraps her in the urn. She then seeks out Grand Pabbie and asks him to erase her sisters' existences from everyone's memories, even though he implies a magical price will be extracted at her expense.

After marrying her husband, they rule as Queen and King of Arendelle and give birth to Elsa and Anna. When Elsa exhibits powerful and dangerous ice powers, the couple travel to the nearby land of Mist Haven to find a wizard to get rid of her magic. On the return trip home, the ship is caught in a maelstrom. Realizing neither of them will make it out alive, Gerda hastily writes a note, places it into a bottle and throws it overboard in the hopes Elsa and Anna will find it. Soon after, the ship capsizes and sinks, drowning them.

Gerda's message winds up on the beach of Storybrooke 35 years later. A recently thawed out Anna finds the note and brings it to the Snow Queen's cave. There she reads it to Ingrid, Emma and Elsa. It explains that the couple was wrong to keep the two girls apart and to hide Elsa from the world. Gerda also explains that she feels guilty about what she did to Ingrid and wished that that she could take what she did back.

Trivia

 * Many fans have noted that Anna and Elsa's father bears a striking resemblance to Walt Disney in his younger years.
 * It should also be noted that like the King, Walt had two daughters, Diane Marie Disney and Sharon Mae Disney.
 * In the Frozen book illustrations, the king has dark hair and the queen has light hair, but in the movie, it's vice-versa.
 * Iduna's character model, upon closer look, is simply a recolored and customized version of Elsa's coronation appearance, such as her wearing her hair in a crown-twist bun (only with brunette hair instead of platinum blonde hair). There have been several differences, including her clothing and dark brown hair, and her face is thinner than both of her daughters, but her face and eyes mirror Elsa's.
 * The ship that the King and Queen were on resembles the ship Ariel and Flounder were exploring in their introductory scene in The Little Mermaid.
 * In Once Upon a Time, the queen is named Gerda, which was the original name of the heroine in the original "Snow Queen" fairy tale, who was the inspiration for her daughter Anna.
 * According to the book A Frozen Heart, Iduna has a sweet tooth.
 * After her death, Iduna's belongings were stored within the castle passageways.