Mors is not the Hooded Man, but I do believe he is in league with the Mance, along with many other Northmen.
Apparently, Melisandre wanted Jon to send Mance to rescue his sister in order to gain Jon’s trust, but the especially curious issue here was that Melisandre saw Arya riding north, east of Long Lake, and Mance said he had a ploy in mind, asking for a handful of spearwives to help him, suggesting he knew that he would be going to Winterfell not the eastern shore of Long Lake. Later we found out with the arrival of Alys Karstark at Castle Black, that Mance did not even bother to look for Arya, and Jon began to suspect that Melisandre had some other task for Mance. He ended up thinking about Melisandre’s secret agenda at least twice more.
Disguised as Abel, an echo of Mance’s hero, Bael the Bard, the Mance wanted to know how Theon captured Winterfell. Clearly, Mance was attempting to find some way for Stannis to capture Winterfell. He also wanted Theon to show him the crypts. While Mance was apparently unable to find some way for Stannis to capture Winterfell by some trick, his spearwives began murdering men to fan the flames of animosity between House Frey and the Northmen, especially House Manderly. Presumably, Mance intended to hide in the crypts as Bael had done.
But why was Mance so eager, desperate even, to help the presumed Arya to escape? He did not seem to care about Theon, but he needed Theon to get the presumed Arya out. Did he believe that he had stumbled upon Arya Stark at Winterfell, and that he needed to get her out of the castle to fulfill Melisandre’s vision to foster good relations with Jon and to promote fidelity between the Free Folk and the North? Is that why he apparently sacrificed himself to free the presumed Arya? Theon was quite convinced that Abel would be caught and flayed by Ramsay, and that fate was apparently confirmed in the pink letter
and foreshadowed in The Dornishman's Wife.
Interestingly, one of the spearwives, Rowan, seemed to hold Theon in great contempt. This alone would not have been suspect, but she also took great umbrage at Theon’s use of House Stark’s words, suggesting she was actually a daughter of the North rather than a native of the Free Folk, although there did seem to be a grudging respect, or awe, for House Stark among the Free Folk. Rowan, tall and skinny, too lean and leathery to be called pretty, but attractive with auburn hair, could very well have been the daughter Mors lost during a wilding raid.
Perhaps Mance stoped at Last Hearth with Rowan on his way to Winterfell. Perhaps Rowan convinced her father that he should not be demanding Mance’s skull for a drinking cup after all.
Mors later arrived at Winterfell. He did not attack, but he started blowing war horns, presumably to instill fear in the defenders, but possibly to alert agents on the inside, and notice that was precisely when Mance decided it was time to bug out.