Olaf finds Anna and helps her realize that Kristoff loves her. He helps her make her way to Kristoff who has had a similar realization and returned to tell her. But, as the storm stalls Anna also sees Hans about to kill Elsa and instead jumps in the way. This gambit works since she freezes into a solid block of ice. Elsa is distraught because she has gained and lost Anna again. Anna thaws, since this sisterly sacrifice is also an act of true love. And now, each having found a little balance between emotion and suppression, Elsa figures out how to control her powers and Anna helps send Hans back to his kingdom, and also kisses (but does not, as far as we know, immediately marry) Kristoff.
Hans had imprisoned Elsa but she managed to ice over her chains and escape. Hans catches up to her and tells her Anna is dead. Distraught, Elsa turns away and doesn't notice he's about to kill her.
Anna tells Hans the situation, and he reveals, that actually, he doesn't really love her. He just wants her for her kingdom. Oops. So, he locks her in the room and tells others, including Elsa that she has died leaving him in charge.
While the book version of Sense and Sensibility is a little less overt about Colonel Brandon, the Emma Thompson version of the movie has him retrieve Marianne who is so distraught over Willoughby, she is lying out in the cold and rain. In "Frozen", Anna and Kristoff both agree that if Anna needs love, then she needs to be with Hans, so, as Olaf points out later, Kristoff loves Anna enough to rush her to Hans and then leave her behind. (I will refrain from pointing out that I'm not sure of the passage of time here, but Anna and Kristoff also don't seem to have known each other that long. Yep, refraining.)
As Anna begins to show symptoms of being frozen, Kristoff takes her to his stone troll family. They assume Kristoff and Anna are a couple and try (in song) to convince the pair to give each other a shot. The trolls (who Anna and Elsa's parents had brought her too the last time she was iced) are unable to help this time, and advise that an act of true love is needed to save her.
In Sense and Sensibility, after neglecting herself to the point of illness, Marianne comes to see that perhaps passion just for the sake of passion has its flaws and eventually comes to appreciate the charms of Colonel Brandon.
Anna, unused to having people to talk to, falls completely for quite literally the first guy she talks to. While admitting getting engaged seems nuts, she remains committed to the idea even after the news causes her sister to ice the kingdom and she runs off leaving her brand new fiance in charge of the kingdom. (I could write a whole other post about how this kingdom hopefully runs itself pretty well given how carelessly it's leaders seem to trade off, but I shall resist. For now.*) Anna hasn't had a friend her own age since her sister was told to hide her power, so the connection she feels with Hans is magical. Other people who suggest she should wait and get to know him don't understand that Anna can't count on other days to meet people. (Sure, now that Elsa has abandoned the kingdom, she could go back and leave the gates open, but it's still an unfamiliar concept to her.) On her journey she encounters Olaf the snowman and Kristoff the mountain man. Anna talks easily with Kristoff and gets along with him, but has to nudge him to help her find her sister so their relationship does not seem as easy.
In Sense and Sensibility, Willoughby must suddenly leave town. Marianne continues to write him letters and does not stop until her letters are returned to her along with other tokens, and she learns he is engaged to another. Later the Dashwoods learn that Marianne is not the first woman Willoughby has made promises to (or suggestions of promises, given Marianne later admits they were never actually engaged) that he ultimately did not keep, have abandoned another young woman after impregnating her. (And yes, there is an interesting division in the suitors, Elinor's was circumspect given that he was technically engaged even risking disinheritance, more committed to honoring his commitments whereas Willoughby was freely passionate, although in his case, he was not willing to risk disinheritance by marrying anyone not of fortune.)
In "Frozen", Elsa does not have a love interest, but in the mountains now has the freedom to go all out with her powers. When Anna tracks her down to tell her about the winter, she cracks again. (No pun intended.) Having thought being outed and outcast freed her to be herself and do what she wanted (which as an heir to the throne with a giant secret to keep had to be so relieving) she now discovers she has caused a problem she doesn't know how to solve. Reminded that her power can be dangerous she tries to send Anna away so she can't be harmed, but unbeknownst to both of them has iced Anna again, this time her heart.
In "Sense and Sensibility", Elinor manages to maintain her outward calm, until she is led to believe that Edward has married. She breaks down, regretting not demonstrating herself more strongly, despite his pre-existing engagement. She finds later that Edward has been jilted, and it is his brother that has married, leaving him free to propose to Elinor.
Anna, on the other hand, is so excited to finally have people to see and talk to. Knowing that the plan is for the gates to shut again tomorrow, she's trying to cram a whole lifetime of experiences into a single day.
Their parents die (sorry, Disney movie parents, you seemed lovely), and Elsa, as eldest, ascends to the throne. Coronations demand things like, well, witnesses so the castle gates get opened up for one day and Elsa and Anna have differing reactions and expectations. As demonstrated through the song (and sidenote, this is one of the things I think the musical form lends itself so well to, showing in duet form emotions surrounding the same event) "For the First Time in Forever" Elsa is trying to remain calm, reign everything in, knowing that all these people with all their eyes on her puts her at huge risk of exposing her power, which as she has been told "conceal, don't feel" her plan is to try to not feel anything for the day.
But the more I ponder it, the clearest comparison seems to me to be Jane Austen's Sense and Sensibility. In Sense and Sensibility the Dashwood sisters have arrived at differing extreme approaches to life - one of logic, one of emotion. In "Frozen" Elsa's mishap injuring Anna with her ice powers and as a result, their parents decide to lock up the castle and Anna's memories of her sister's powers are removed. So, Elsa is encouraged to work on suppressing her feelings to gain control over her powers and Anna is left mostly to her own devices. So, Anna remembers that there was a time when she and her sister had fun and played and people got to visit the castle and now her sister seems to ignore her and everything is shut up.
Note: I will be discussing "Frozen" and Sense and Sensibility, so therefore revealing plot points of both.When I saw "Frozen" last winter, it lived up to all my hopes. On leaving the theater I had noted the way "Enchanted" handled the true love kiss issue and that I appreciated for "Frozen" they went a slightly different direction . And I found myself on the Disney Wiki reading comparisons to things. I see their point about some of the comparisons to "A Little Mermaid" (although I would argue that a lot of Disney movies open with a setting song).
In Sense and Sensibility, Elinor is so guarded in her expressions of emotion, afraid of seeming to forward, or of revealing unrequited feelings, that at times her family is unsure of her attachment to Edward, and her sister-in-law tells people she's just after his money. Marianne, on the other hand, ignores Colonel Brandon who to her seems too old to be passionate (at, ahem, 35) and has no trouble displaying her feelings for Willoughby, such that her family wonders if she has gotten secretly engaged.In "Frozen" Elsa manages to just make it through the ceremony, but Anna who has managed to go an fall in love with practically the first guy she sees and now thinks they have the most amazing connection and wants to marry him even thought they've just met. (The characters repeatedly reference a day, but honestly, while it does go from daylight to night, I think it's still safe to count how long Anna and Hans have known each other in hours.) Elsa is so horrified by this, she loses control and ices over the ballroom, and eventually the whole kingdom. She runs off into the mountains, where finally she feels like she can, as the song says, "Let it Go".
So while Sense and Sensibility has some additional secret engagements, and significantly less snow and ice than "Frozen", ultimately the lessons the sisters learn in each are similar. Both learn that the extreme approaches on both sides carry risks, and a balanced approach leads to greater happiness and love. Two very enjoyable approaches to this.
*In the Script Notes podcast, Jennifer Lee mentioned that there were things like who was running the kingdom that they had answers for but that got cut, because it wasn't germane to the core plot. I get this. I just, still wonder.