I have absolutely no idea if this is part of a mod or part of the vanilla game, but ever since I defeated Miraak I've been seeing this odd looking lady Dragon Cultist everywhere. She doesn't wear the same cultist outfit as the others and isn't hostile. On the contrary, she just stands around and only says hello when I try to talk to her. She's dressed in Ancient Nord Armour with a helm decorated with deer antlers. The only other thing I've witnessed her doing is making dragon shouts. Any idea what she's all about?

Sounds like a mod, unless you have a glitch where one of those dragon cultist women ghosts are following you.

In all my hours of playing I've never seen this lady. Either It's due to a mod or I'm not looking hard enough.

I do not recall seeing her, although I do remember some person with ancient nord armor but I do not remember where. I am presently doing the Dragonborn quest, and I will look for her after I do away with Miraak. Is there a certain place you see her the most??

Never heard of any woman dragon cultist ghosts...

Do you have a screenshot of her?

M'aiq thinks it is most likely a mod.

If you want, M'aiq could take the lady away from you..

M'aiq should meet Narfi.

Narfi talks like khajiits.

That sounds a lot like one of the http://www.uesp.net/wiki/Skyrim:Dragon_Cultist from Forelhost. Either way, the problem sounds like it is mod related (as others have said), unless you have experienced an very rare bug.