It's a little hard to pin Katharine down, because some editions attribute more wordplay to her than others. Berowne's first banter session with a woman is either with Katharine or Rosaline—and that decision affects how we view Katharine. Either way, she wrangles with Rosaline in Act 4, Scene 2, and, after this, we see her as the third in command.
She has reason to be wary of love since it killed her sister, and takes out her aggression on poor Dumain's letter, calling it a "huge translation of hypocrisy,/Vilely compil'd" (5.2.28). She shows him more mercy at the end of the play, though, demanding no fasting or service—only that he wait.