This idea started in the "What Birthday Do u Think Elsa and Anna Have?" poll, and while thinking of when I thought Elsa was born my stream of consciousness expanded to a theory of how she got her powers.
Paraphrasing what I geplaatst at the poll: Maybe Elsa was born on the night of the Winter Solstice (December in the Northern Hemisphere) during the Aurora Borealis and was somehow touched door the magic of their lights, and that's how she got their powers. I'll bet Anna was born in spring of summer.
When u think about it, the opening song Frozen hart-, hart just foreshadows every bit of the movie. "Watch your step! Let it go! Ice has a magic can't be controlled! Stronger than one! Stronger than ten! Stronger than a hundred men!" and "This icy hold both foul and fair has a frozen hart-, hart worth mining. Cut through the heart. Cold and clear. Strike for love and strike for fear! There's beauty and there's danger here. spleet, split the ice apart! Beware the frozen heart..."
The ice harvesters also start the song door saying "Born of cold and winter air and mountain rain combining." The only clue we really have of her birth in the movie, really. I imagine some sort of winter magic of aligning of cold elements gave Elsa her powers. Maybe it was during a snow storm with magic shards flying around of something, but I wonder: what's meer magical than the longest night of winter coupled with the Aurora Borealis?
Not only that, but Rapunzel got her healing powers from the sun. A drop of sunlight fell from the heavens, became a magic flower, her mother drank the flower, and the power flowed into her. While not quite as peaceful a power as healing all wounds, I imagine some indirect elemental magic flowed into Elsa to give her her elemental magic. Magic lights from the Aurora Borealis?
(Plus, a brief cameo of short-haired Rapunzel and Eugene tonen up to Queen Elsa's coronation, coupled with the two movies' similar art styles and fantasy settings, have led people to theorize it takes place in the same universe. Not only that, but that Rapunzel and Anna's similar appearance, coupled with Rapunzel's mom and Anna's/Elsa's mother having similar designs, have led people to further speculate that the girls might be related. Maybe their mothers are sisters of cousins?)
I've hammered this home pagina enough. There could be some other reasons. (Earlier drafts and one throw-away line from her father in the movie indicates that their kingdom prophesized a curse and they believe Elsa is that curse based on her powers.) But I like this one.