Kevin

In HTTYD 1 we get this very emo lookin cut. Since the first movie is told through Hiccup's POV, it matches how he sees her: unapproachable, scary, and tough. Even the back of her hair, it's tied up tightly to show her uptight and no-nonsense attitude.

But after she sees Hiccup for who he is, she pushes her hair out of her eye so he can see her entire face. Almost like she's "letting him in", if not to be cliché. He gets to look her in the eyes when he talks to her, whereas before he avoided her stare.

Then we get to RTTE and her fringe is shorter and doesn't completely cover her eye as much. Her hair is much softer, showing how she herself has softened (preferring capture over kill missions as she says). And the back of her hair is looser and bounces about the place.

In HTTYD 2, there's not a huge change because RTTE happens pretty close to the second film but her hair is on the side now. You could take this as her being less uptight and war obsessed because a braid on the side isn't very practical for battle but she's a lot more relaxed about it now. Edit: also there hasn't been as much war in the last 5 years than there was before HTTYD 1 so choosing aesthetic over function is a lot easier to do. She doesn't have to sacrifice her beauty anymore for the sake of fighting.

And in HTTYD 3, her fringe is out of her face and her hair is fully let down. She's relaxed and comfortable with her femininity as well that she's so toned back from how angry she used to be in HTTYD 1 like she said, "I'm the person I am today because of you," - it really shows the effect her relationship with Hiccup has had on her. That he's made her comfortable to embrace her feminine side.

(side note, her hair in HTTYD 3 was gorgeous)

And you could even say her marital braids represent Zephyr and Nuffink.

“Binder taught this child how to nuture and grow.”

“Do you think my father allowed me reverence for life?”

“I do not even know how to grieve.”