Maybe because she is inside looking out. Her eyes are doing the moving. http://www.norskengelskordbok.com/en/dictionary-norwegian-english/ute
I wonder if she were outside looking around at the great outdoors how that would be said?
I didn't even know that existed! Thank you! http://www.norskengelskordbok.com/en/dictionary-norwegian-english/sees
It can mean "to seem/appear", and that's when it tends to get split up:
"Du ser nydelig ut!"
"You look lovely!"
"Den ser ferdig ut."
"It looks [ready/done]."
...unless a conjunction is used to liken something to something instead:
"Katten din ser ut som en hund."
"Your cat looks like a dog."
It can also be split up by an adverb when meaning "to look":
"Hun ser alltid ut vinduet".
"She's always looking out the window."
It's possible to use the reflexive version "å se seg ut" to mean something in the ballpark of "to choose", but it's really closer to "to have one's eyes (set) on".
"Han har allerede sett seg ut en ny bil."
"He already has his eyes set on a new car."