I was able to attend a work in progress screening of the film during the late summer last year, Do You Wanna Build a Snowman was still storyboards, Frozen Heart and In Summer weren't yet integrated, and none of the final audio recordings were implemented for any of the musical numbers, but something that might interest some of you is an extended opening that was present in this version. In place of Frozen Heart, there was a montage, narrated by the elder troll, that explained how when Elsa and Anna's family came into power many generations before the film takes place, the new king made a sort of pact with the trolls, promising to protect them and keep them secret from anyone looking to exploit their powers or use them for otherwise nefarious purposes. In turn, the trolls ensured the king's family a lengthy, peaceful rule, in the form of a prophecy given by an elder, ensuring the family would come to know a great power (alluding to Elsa's magic).
Generations pass, Arendelle grows and expands, the prophecy's meaning becomes lost on not only the family of Arendelle, but also the trolls, and Elsa is born. Her crib freezes over during a hot summer night and the King and Queen are understandably distraught, though the baby is fine. The King spends what looks like days in the family's library, looking at medical recordings, trying to find any information on what could have happened, or if it can be explained. Eventually he finds several dusty books about the trolls, including some passages written by the First King. He becomes distracted and reads it all before the Queen requests he stop because the baby seems fine.
Elsa's magic continues to show, to grow, but the King and Queen decide to just keep a watchful eye as it doesn't seem to be causing any harm. Then Anna is born, and there are a few brief scenes that show Elsa entertaining the baby with little icy fireworks. Jump ahead a year or two, to Anna waking Elsa up, and the snowman scene from the finished film.
After the screening was over there was a Q&A session, mostly to talk about technical aspects of the film, like particles and lighting systems, though some story elements were also discussed. The crew members that were present at the screening explained that the entire prologue was at risk of being cut because it was too lengthy, and distracted from the focus of the two sisters. It's only purpose was really to sort of explain that Elsa's magic came from the family's agreement with the trolls, but after some thinking, the crew had decided it didn't need to be explained, just as "the enchantress who cursed the Beast never needed an origin story, and the Genie didn't need to be explained" (that's about as close as I can remember the actual quote).