Is Harwin the Hooded Man inside Winterfell?

Right, so this theory is based upon Harwin being the Hooded Man that Theon encounters at Winterfell. HM: “Theon Turncloak. Theon Kinslayer.” Theon: “I'm not. I never... I was Ironborn.” HM: “False is all you were. How is it you still breathe?” Theon: “The gods are not done with me. Lord Ramsay is not done with me.” HM: “I leave you to him, then.” This theory is based off the movements of the Brotherhood without banners. During A Feast for Crows, we learn that Tom Sevenstreams is sent to Riverrun to spy for Lady Stoneheart. Tom follows Jaime after he requested that Tom plays the Rains of Castamere to Edmure Tully. Tom learns two things when with Jaime 1.) Ryman Frey, Lord Walder’s heir, is leaving Riverrun, likely to return to the Twins. 2.) The Red Wedding hostages held in the Twins may soon be transferred into Lannister custody and presumably taken to King’s Landing. A possible third discovery is that Jaime is a competent commander, the only man with sufficient authority to bring the quarrelsome Freys to heel. Tom wastes little time, no more than the two days or so it takes Riverrun to surrender, contacting his fellow outlaws about Ryman’s travel plans. By Jaime’s next chapter, Lady Stoneheart has ambushed Ryman and his party. This means that if she sent Tom O’sevens to Riverrun it is highly likely she would send someone to Winterfell after hearing that Arya is alive from Harwin. With news of ‘Arya’ being married to Ramsay Bolton, who better to send up North than Harwin? He knows Winterfell, he knows Arya and would be able to report to LS if ‘Arya’ was actually Arya. Also, the HM calls Theon a Kinslayer. Who else would know how close the Starks and Theon were? Everyone else who lived in Winterfell is either dead or scattered. It makes sense that LS would want someone to keep an eye on ‘Arya’ and to aid her if/when the opportunity arises to help her escape. The actions of the HM also match the actions of a LS led BwoB. Killing Freys. It is LS’s mission to kill anyone who she believes to have anything to do with the death of her husband and sons murder, as shown by the hangings of Petyr, Merrett, and Ryman Frey.