You can make her take it down,give her armor or a piece of armor(It worked for me with armor,don't know about pieces) indoors and then go outside and she won't have the hood anymore.
You can make her take it down,give her armor or a piece of armor(It worked for me with armor,don't know about pieces) indoors and then go outside and she won't have the hood anymore.
But It's permanent.
I gave her forsworn armor,vampire royal armor, normal and flawless. The only time she wore armor was when I gave her my own legendery daedric armor.