She may or may not have. Nobody is really sure what happened. There are just rumors and I doubt Howe was bragging to his allies about what he did. Also, even if she did know what did you expect her to do? Insist on trying to murder Howe herself? He had too much power to be touched politically and brought to justice that way by a mere knight. Resign from Ferelden's service because Howe is evil?
Okay, end of discussion. When you even think about the idea of Cuthrien not knowing about Howe's deeds, it really looks like you are more of a Cuthrien fanboy than someone interested in a serious discussion.
But Cauthrien shows up to arrest you for something you actually DID do: killing Howe. Do you really think that murdering an Arl is legal? If it is then Howe's actions killing a Teyrn would have to be similarly legal.
First of all, Cuthrien does not know that the Arl is dead, that's impossible. She goes there because Loghain knew what the Warden is up to and told her that the Arl is already dead yet neither Loghain nor Cuthrien have a single proof of Howe's death - even Anora does not know anything about his fate.
Secondly, you still miss the point. Howe killed Teyrn Cousland
FIRST, this
meaning he killed the HN's father BEFORE the HN kills Howe. As a consequence, the HN has blood right, allowing him to slay the murderer himself as his father and basically the whole family was not sentenced to death by an assembly but murdered for political reasons. It's not THAT hard.