There is supposedly one example of this
Spoiler when wearing Thalmor Hooded Robes is supposed to help get you into their Embassy undetected.
But yeah, I always laugh when I Smith up a completely new set of armor, with fully-covered face, which nobody has seen before...
And right away a merchant says "you've been a good friend to me..." LoL
Everyone immediately knows who you are

Hey I guess you can never hide when you're as famous as The Dovahkiin...