Hmm. I hope you don't mind me sharing my two-cents, but we have actually seen Elsa's character both because of her magic and outside of her magic.
She is creative. She does not just create like a 3D printer with her magic, and you can tell by the little accents here and there. In the first film, her ice palace and her dress have Arendellian accents on them showing that where she is and what she knows impacts what she creates. She can actively change the style of what she creates. With every dress she wears, she adds a little accent here and there. It's almost like a cross between snowflakes and Arendelle until she enters the Enchanted Forest.
She is introvertive. You can just see it in the way she behaves. She is playful and mischievous, but she is not Anna. Anna was bombastic and enthusiastic to Elsa's more thoughtful nature. She is always a little quieter and reserved compared to her sister. Even as a child!
She is intelligent. Despite her very restrained childhood, Elsa was also raised to be Queen of Arendelle. In the little parts where we see it, Elsa can do her job well. She starts making trade decisions right at the end of F1 with Weaseltown. She creates community events for the kingdom (ice rink at the end of F1, Anna's birthday, OFA). We see her easily slip into that regal and reserved queenly nature when Kai comes to find her. She also is rather strategic when fighting the soldiers infiltrating her castle in F1! She is detailed, specific, and controlled. She can think quickly on her feet. When she fights the spirits, she is the same way. She knows how to conquer them or control them - with or without her magic.
She seeks spirituality.
- "I am one with the wind and sky."
- "Or are you someone out there
Who's a little bit like me?
Who knows deep down
I'm not where I'm meant to be?
Every day's a little harder
As I feel my power grow
Don't you know there's part of me
That longs to go."
- "My magic can feel. I can feel it."
-ALL OF SHOW YOURSELF
-The way she talks to Anna at the end of F2
-How she handles the spirits, as if she knows them
Our girl is seeking a higher understanding. A higher answer. In the mythic storytelling of her characterization, she makes these grand proclamations. These grand showstoppers and these grand realizations. Elsa is mythic and within myths, it is all about sacrifice and magic and faith and destiny. For Elsa to understand her magic, she had to sink deeper into the spirituality of her mother's people. And with "I am one with the wind and sky," it shows a sort of self-awareness of the mythic quality of her magic... as much as the wind and sky itself. She knew even then.
She is playful and mischievous. This carries across as one of the most obvious characterizations Elsa has. When she is coronated, she playfully pushes Anna into dancing with the Duke of Weaseltown. At the end, she gets Anna to go ice-skating despite Anna's initial refusal. She is kind, don't get me wrong! But she also will play around and Anna can measure up!
She is selfless. To a fault. Everything she did for 13 years was bend over backwards to protect Anna. She repressed all that she was in order to keep everybody safe. She hid herself up in the mountains to protect everybody safe. That was confirmed not by her magic, but outside of it. Her behavior was influenced by her parents, absolutely. However, Elsa kept up with it into adulthood after her parents died. She kept up with it even though she had the first warm moment with her sister in years at the coronation.
There's more, but I am getting tired. My two-cents!