If there are people who think about this, the look Anna wears when she first sees Kristoff is not based on a feeling of a princess feeling superior about her social status. Since Anna is a kind, caring person who likes people, she likes to meet new people and make new friends with almost anybody and everybody she meets. During different parts of the movie, we see her interacting with the townspeople and she shows no disregard for those who aren’t figures of royalty and nobility. So Anna in no way looks down on commoners or people of lower classes, including people like Kristoff. When she meets him, she isn’t looking to fall in love with him because of the views she has about love with a man; in other words, she initially saw Kristoff as a person who could be her friend (despite his grumpiness) rather than her boyfriend.
Before she actually meets Hans, Anna is briefly angered by the fact that his horse rammed into her and made her fall into the boat. But then when she gets her first look at him, she immediately becomes entranced by his handsome appearance and graceful, polite manners, especially when he helps her up and bows gallantly to her. Because his looks and charm quickly make a good impression on Anna, which then leads into their seemingly mutual attraction for one another, she and Hans hit it off right away (even in a literal way, because it started when she was hit by his horse! XD). Later, they spend the entire evening together, talking, dancing, singing, and getting along even more, especially because they appear to be so much like each other. When Hans proposes to her, Anna considers it the biggest, luckiest, and most perfect moment of her life, and to make it even more perfect, she, of course, accepts the proposal.
On the contrary, when she first meets Kristoff, Anna looks at him with some confusion, disgust, and even mild fright. But the reason why she does isbecause he looks like a scary snow monster and he doesn’t say hello to her or Oaken. He remains rude by refusing to make conversation with either of them, then gets annoyed and answers in a gruff voice when Anna asks him about the North Mountain (since he is trying to make a bargain with Oaken and is getting cross that he can’t). Shortly afterwards, Kristoff refuses to take Anna to the mountain until she reveals that she bought the items he wanted. Then while riding in the sled, Anna argues with Kristoff when he expresses his confusion and shock about her engagement, since she doesn’t see why it is a big deal or understand why he thinks it is. When the wolves pursue them, they continue to bicker over the matter, and Kristoff gets annoyed when she throws the lit blanket and tells Sven to jump. Finally, he becomes upset when his sled is destroyed, since helping Anna has caused all of this to happen.
So when Anna first meets Hans, they “fall in love at first sight,” and subsequently get along so well and so fast. Later, they only continue to get along and are not shown to have any arguments. In short, their entire relationship goes smoothly, flawlessly, and without any problems; it has been completely perfect, and so it means (in her mind) that it will always be perfect. Thus, it is why (among the other reasons that I have shared before) Anna thinks Hans is her true love. He is her living dream prince, though him being a prince is certainly not the sole reason of why she believes they have true love. Maybe she dreamed about having her own prince to marry, but it’s possible that Anna did not limit to that when she said she wanted “a chance to find true love.”
But with Anna and Kristoff, things are very much the contrary during their first scenes of being together. They do not form any real sort of attraction when they meet. Anna remains kind and friendly, but Kristoff is gruff and crabby, and only helps her because of a bribe. Nothing goes smoothly and perfectly afterwards because they don’t agree, and argue, about Anna’s engagement, then the wolves attack them. So because she and Kristoff had a bit of a rough start, completely unlike how things went between her and Hans, this is why she did not think she would fall for Kristoff. It never had anything to do with the fact that he is a commoner and she is a princess (who already had “the prince” as her fiancé).
But by the end, of course, Anna has learned a harsh lesson about how love was not at all what she thought it would be, especially based on her first impressions with both men. Hans may have seemed noble and polite, but he was really a ruthless, sadistic sociopath with a heart of ice (get the joke? XD), and her last impression of him included a punch in the face. On the other hand, Kristoff acted gruff and grouchy, but he was really a selfless, caring man with a heart of gold, and Anna’s last impression of him included a kiss on the lips. :D <3
Couple things I never see people noticing in Frozen...
1: After Hans gets sucker punched by Anna, he falls into the water. Funny how, for a deceiving murderous Prince, they took the time to change him back to dry clothes before shoving him into his makeshift cell. I figured they’d just let him sit in those damp clothes and chafe. That’s what I’d do. LOL
2: This probably is one that’s actually noticed, but when Kristoff kisses Anna, at first she makes a surprised whimper, but then she makes a cute little happy sigh as she kisses him. I thought that was adorable, and a nice touch, but I never hear about it.