I've noticed an amusing bug where Olda in Dragon Bridge will be outside her house in her underwear.

Woo-hoo!

In all seriousness, though, this appears to be a fault with the AI. I've noteced a handful of times where spawned NPCs will not have equipped the items that are in their inventory (typically clothes.) It's not all that common of a bug, and existed pre-Dawnguard, so I know it's not a recent thing.

I'm running SKyrim on the PC, too, so it's just not a 360 thing.