This happened to me, too, but it was the other way around. I gave her items inside when she had no hood, and now she refuses to wear it outdoors....
I got this too, but she went back to hood-wearing after the next Fast-travel.
Although, you just gave me an idea. I'll try it soon.

Edit2: OMG It worked. I think I love you. I gave her whatever I want her to wear indoors with no hood, and now she's hoodless! Wootcakes. Let's hope its permanent.