This analysis contains spoilers from the mentioned films and possible spoilers from films to come (yes you read that correctly). To avoid confusion I probably should add that this is a satirical piece with some truth and bit of sarcasm..
I was left with many questions after watching the movie Frozen, and while reasoning out several elements in the story, uncovered some mysterious connections.
First it is important to establish a singularly key fact. The characters of the world of Frozen and the world of Tangled coexist, probably in neighboring kingdoms. This is confirmed by one still-shot from the movie Frozen, showing Rapunzel, Flynn and Anna together. My suggestion is that these two movies are far more connected than what is apparent in the film Frozen, and that that connection shows a much broader picture of the perilous world in which these characters exist.
Since we are referencing the movie Tangled, it is good to point out that we know where Rapunzel's power comes from (a magic golden flower). However in the movie we are discussing here, we do not know the source of Elsa's power, and based on what is mentioned in the film, assume she was born with it. This is a bit peculiar. Could there be other forces at work? Quite possibly so.
In the movie Tangled, Mother Gothel steals away the baby Rapunzel early in the film, and it is not a stretch of the imagination to consider the possibility that Gothel exchanged the true daughter of the King and Queen of Arendelle with none other than the magical baby Elsa. But why? Who would want this to happen? Someone who would like a magical queen to sit on the throne of Arendelle perhaps, or is there even a deeper motive?
Other questions arise after the apparent demise of Elsa and Anna's parents early on in the film. After the unfortunate incident, who is the person who keeps the kingdom in order until Elsa is old enough to assume power? Someone has given the command that the girls should remain cloistered behind the sealed doors of the castle, until the coronation of Elsa as queen. With a limited staff in the castle, and seeing no other characters assume the role as steward of the kingdom, it is quite possible that this order was reinforced by none other that Elsa herself. This, however, would require her having authority and control, not only of the kingdom but of her powers.
This is a strong claim since the movie's premise is built on Elsa's inability to control the icy gift of freezing water and covering green Summer fields in snow. Which leads us to another question. Why would she do this? Why would she show such weakness, and such a strong inability to control her magic powers? For the answer, we simply have to turn to the result of her actions. What happened in the film? The exposure of hidden evil.
And now we come to the villain none of us suspected. The treacherous monster everyone knew and loved as Hans, the handsome hero from the Southern Isles, who tricked the poor Anna with his dashing looks and catchy musical number. The murderous criminal who would stoop low enough to kill the two female protagonist of the film so he could claim the throne. As described in the movie, Hans had twelve brothers. They seemed to have made it well in the world and had turned their backs on their youngest sibling, leaving him to perform dastardly deeds to seize power. This my friends could be the key.
So here is my theory. Elsa was placed in line for the Arendelle throne by the powerful and mysterious "Brothers of the Southern Isles" (possibly with magic powers themselves since they seem to direct magical entities), not only because her power would secure Arendelle but also to draw out the weak link, Hans, who had become a loose cannon, and threatened the stability of the continent.
Maybe you doubt the theory because of the movie's harrowing end. If you have an objection to my hypothesis based on Elsa's actions, as Hans was about to deliver his deadly blow in the final scenes, perhaps you should consider that none of us know what truly happens when you strike the Snow Queen with a cold steel blade.
Hans would have most likely frozen to the ground, immovable for ever. In fact it appears Elsa's power flowed through Anna, knocking back the assailant Hans, and inflicting dramatic results on the poor blonde defender. Might I also state that it is quite possible that Elsa was the one who thawed the frozen Anna, and after a quick recovery restored the kingdom to it's natural temperatures in approximately thirty seconds. This shows us what? Complete control of her powers.
Thus ends the observation. I can't wait for the movies that will follow this one! Below is another possible title for this movie that fits well with the subplot, don't you think?
Other interesting points to consider:
Hans is not frightened away by Elsa's powers and moves forward with his evil plans, leading us to believe he is quite familiar with this sort of display. It is possible he has witnessed similar spectacles from his magical "brothers."
Elsa hits Anna with a cold blast to the heart, and shows little emotion beyond a slight gasp. This was an intentional move to freeze Anna temporarily and keep her protected until the evil Hans had been dealt with. Unfortunately she was too close when Hans made his deadly move against Elsa, causing Anna to freeze rather than Hans, who was blown back by a power blast.
Elsa's original plan nearly worked as Hans was willing to travel with Anna to search for the Snow Queen, essentially bringing the villain to meet his fate in the icy trap Elsa had prepared.
The foreign dignitaries can be seen on the balcony laughing and applauding as Anna punches Hans off the side of the boat. These same dignitaries appearing deceived were working innocently with Hans a few minutes before and would have no idea that he was evil. At least they would have been bewildered by what had transpired. Conclusion - They knew Hans was evil and were working with Elsa all along.
The mysterious Icebreakers at the beginning of the film had eerie green lanterns, similar the one used by Mother Gothel in the film Tangled, showing yet another possible connection.
Finally as mentioned before, Elsa makes short work of the snowy spell at the end of the film with little effort at all. This is after she has made a castle out of ice and wardrobe, including ice skates, which appear to be made out of a more substantial substance. This would lead one to believe that her powers extend beyond snow and ice and that she has complete control.
