What MBTI type do you think Elsa is (explain why)?

I agree with you that Elsa is an ISFJ. This is a description of N and S I got from 16personalities.com

Intuitive (N) – imaginative, rely on their intuition, absorbed in ideas, focus on what might happen.

Observant (S) – down-to-earth, rely on their senses, absorbed in practical matters, focus on what has happened.

Clearly Elsa is an S. She relies on her senses and focuses on what has happened (her power is dangerous, she has attacked Anna). She never thinks that she can use her ice powers for good. She is not dreamy and imaginative. She has no idea how to solve the problem she created.

Besides, ISFJ is classified as a "Sentinel" and INFJ is a "Diplomat". Elsa is more of a Sentinel than a Diplomat. She is very protective and traditional. She wants to be the "perfect girl", obeys rules and traditions, and tries to fulfill her duties.

I think she is INFJ, and I will explain why. First, I agree with you to say that she has Fe. Elsa is altruistic, she locked herself in a room to keep her sister and her kingdom safe (Fe). INFJ are called "The Protector", after all. She needs to express her feelings, which are correlated to her powers. If she was an Fi user, the rule "conceal, don't feel" would be easier for her. We can see that she is a very warm and soft person who lives in fear. She cares deeply (too much) about others. Yes, Te users can, but it's plus common for Fe types, who constantly think about others before themselves. She also wants to be a good girl, being perfect because of Fe, not Si. If it was Si, she would not be so... depressed. She follows the rules just because she thinks that she is a monster, and so her acts are restrained because of her fear of hurting others. She fears the future because she does'nt have much self-confidence, and also because the troll said that " Fear WILL be her enemy". It's pretty scared. When her parents and other people see her power as a bad thing, Elsa hates herself, but when she is accepted, she finds self esteem. And she's more afraid of Se (part of her power which she can't control) than the future.

In fact, she is not capable to balance her Ni and her Fe. When she uses Fe, she ignores her dominant function and when she uses Ni, she ignores her auxiliary function, and lives in her "own world". She is also incredibly creative and artistic when she builds her ice Castle and makes her ice dress (Ni-Se). Some details of the movie show that she particulary loves purple(and blue, obviously). The meaning of these colors is the perfect description of an INFx : idealism, compassion, sensitivity, spirituality, intuition, nurturing tendancies, faith, friendship, mystery... At the end of the movie, Elsa is happy to be accepted for who she is. It's also a parallel to her childhood. She sees her power as a gift, who can make others happy, and not a malediction.

I agree with you. I think she's an ISFJ. She is very sensing, NO intuition. She never looked to the future. She always heard what past said which is to conceal her powers. She did not look to the future at all, she's very living in the now. She's a down-to-earth, not a dreamer. Besides, when I read ISFJ description, really suits her.

So, I guess you are right!

She does look towards the future. Her hiding her powers from Anna was her trying to prevent something terrible possibly occurring in the future. She is also very creative, as seen when she makes her castle, however I wouldn't say she's an INFJ, as she is certainly not Ni-dom.
ISFP makes sense to me, because she's ruled by introverted feeling, which is supported by extroverted sensing, and her tertiary function of introverted intuition is fairly visible, with very little Te.
However, she seems very sensible and realistic. Not to mention her taking action in many situations (wearing gloves, not leaving her room, building an ice castle, fighting the palace guards).
In this case, I can see her being an ISFP. She is very Fi-dom, and not Fe-aux. Elsa hurts Anna in one way to prevent hurting her in another way, so can't see FJ. She also has that IxFP submissiveness. She does what's expected of her instead of making major decisions for herself, with the exception of Let It Go.