This is discussed in the "Art of Frozen" book.
[Michael] Giaimo is an extremely analytical designer, and when he imagined the costumes for the characters, he applied rigorous aesthetic standards. "For Anna's travel outfit, I wanted something that would be really striking and bold, yet elegant," he begins. "She's a princess, and that really blue skirt says royalty, as does the magenta cape. I thought those two colors would be really striking, because there's a rich saturation to both of them. But there's always a little bit of black on the characters: it helps anchor the saturation, so it doesn't float into the atmosphere."
The warmer green palette was reserved for Anna as she grew and reflected her "sunny disposition". Obviously by the point in the film that she's changed clothes, her disposition is slightly more reserved.
Caption:
To reflect her sunny nature, Anna's color palette during her growing years is kept on the warm side. Grayed yellow greens, ochre, and olive dominate.
