An often discussed identity theory is that of the Hooded Man of Winterfell that Theon encounters in ADWD:

Outside the snow was coming down so heavily that Theon could not see more than three feet ahead of him. He found himself alone in a white wilderness, walls of snow looming up to either side of him chest high. When he raised his head, the snowflakes brushed his cheeks like cold soft kisses. He could hear the sound of music from the hall behind him. A soft song now, and sad. For a moment he felt almost at peace.

Farther on, he came upon a man striding in the opposite direction, a hooded cloak flapping behind him. When they found themselves face-to-face their eyes met briefly. The man put a hand on his dagger. "Theon Turncloak. Theon Kinslayer."

"I'm not. I never … I was ironborn."

"False is all you were. How is it you still breathe?"

"The gods are not done with me," Theon answered, wondering if this could be the killer, the night walker who had stuffed Yellow Dick's cock into his mouth and pushed Roger Ryswell's groom off the battlements. Oddly, he was not afraid. He pulled the glove from his left hand. "Lord Ramsay is not done with me."

The man looked, and laughed. "I leave you to him, then." -ADWD, The Ghost in Winterfell

I've read numerous great theories on this subject (which I will mention below), but in this post I primarily wanted to focus on a couple interesting ideas, thoughts I've had.

The Hooded Man of Winterfell: Thoughts/Theories

This identity is heavily discussed and I've read great arguments both for/against the following:

• Theon Durden (Theon was talking to himself, Fight Club style)
• Hallis Mollen (last seen with Ned Stark's bones, which are mentioned the previous chapter)
• The Blackfish (escaped from Riverrun)
• The Clansman that Bran meets heading to the Wall
• Howland Reed (Hasn't been seen in the story yet, knows too much)
• The Miller (Theon killed his sons and his wife)
• Random Northman (numerous northmen in the castle, they all hate Theon)
• Robett Glover (Last seen at White Harbor with Manderly/Davos)
• Galbart Glover (Last seen headed to the Neck with Maege Mormont, knowledge of Robb's will and fake plans)
• Harwin (The BWB has infiltrated Riverrun, why not Winterfell too)
• Faceless Men (With Tycho Nestoris leaving Braavos and heading to treat with Stannis, a FM could have tagged along)
• Benjen Stark (There must always be a Stark in Winterfell, disappeared beyond the Wall)
• House Banefort (only mentioning due to founder, sigil)

As I mentioned, I've read great arguments for most of the above, but it should be noted that all of the above also seem to have some arguments against ranging from logistics, to purpose to numerous of them being easily recognizable by Theon.

A few things I found super interesting

(not arguing for the below over any of the others, just a couple thoughts I had)

Faceless Man

I couldn't find any real evidence for a FM. That said the Faceless Men have infiltrated the Citadel and have the means to get from Braavos to Winterfell. They will be involved in the endgame.

Harwin

I really doubt its Harwin to be honest, mainly bc he seems to be the "translator" for Lady Stoneheart and the Brotherhood with Banners. That said I would love if the BWB had infiltrated Winterfell. They would then have agents in both Riverrun (Tom o' Sevenstreams) and Winterfell, among potentially others. Maybe a different member..

This would mainly be cool bc it could loosely tie the Grand Northern Conspiracy and the Grand Riverland Conspiracy together.

Benjen Stark

Probably one of the more often discussed possibilities, especially due to "there must always be a Stark in Winterfell". With that in mind some quotes do stand out though:

"It was different when there was a Stark in Winterfell. But the old wolf's dead and young one's gone south to play the game of thrones, and all that's left us is the ghosts." -ASOS, Bran II

and with regards to Bran knowing the castles on the Wall (but the implication being that Bran heads beyond the wall ala a First Ranger, and Benjen stays in Winterfell)

You know them better than I do, Bran. Perhaps you should be First Ranger. I'll stay here in your place." -ASOS, Bran III

House Banefort

I truly doubt House Banefort has anything to do with this, but I just found this interesting.

As often mentioned, House Banefort was founded by:

Other houses sprang from the loins of legendary heroes, of whom tales are told to this very day: the Crakehalls from Crake the Boarkiller, the Baneforts from the Hooded Man, the Yews from the Blind Bowman Alan o' the Oak, the Morelands from Pate the Plowman. -TWOIAF, The Westerlands

and:

The first true Lannister king we know of is Loreon Lannister, also known as Loreon the Lion (a number of Lannisters through the centuries have been dubbed "the Lion" or "the Golden," for understandable reasons), who made the Reynes of Castamere his vassals by wedding a daughter of that house, and defeated the Hooded King, Morgon Banefort, and his thralls in a war that lasted twenty years. -TWOIAF, The Westerlands

It is also worth noting that this is likely a reference to the comic book hero Black Hood. There were several possible allusions to ASOIAF when I looked into this character, but also plenty that didn't match up, so I didn't think it was worth mentioning too much.

If interested: Wiki Article on Black Hood

As I mentioned above there are numerous great theories on almost all the others, so I didn't feel the need to rehash here, but feel free to bring them up.

TLDR: A couple "new" thoughts on the identity of the Hooded Man in Winterfell that could support several different options (Harwin, Benjen, etc.)