Background

In TWoW, a lot of things happen ranging from Stannis finding out about the Karstark treachery, to Asha pleading with Stannis and preparations for the upcoming Battle of Ice. One lesser discussed plotpoint is what should happen in the immediate aftermath of the chapter and that is Stannis' discussions with northmen (Lord Wull/Artos Flint) about Theon.

If we remember, Stannis has recently captured Theon/fArya and Theon is believed to have killed Bran/Rickon so the northmen all want vengeance.

If interested: Accessible Weirwood/Heart Trees

Divide Between Stannis' Followers (R'hllor/Old Gods)

It should also be noted that the divide between Stannis' followers has already caused issues/dissent as the followers of the Lord of Light want a sacrifice for better conditions:

"A sacrifice will prove our faith still burns true, Sire," Clayton Suggs had told the king. And Godry the Giantslayer said, "The old gods of the north have sent this storm upon us. Only R'hllor can end it. We must give him an unbeliever."

"Half my army is made up of unbelievers," Stannis had replied. "I will have no burnings. Pray harder. -ADWD, The King's Prize

and:

"What has your southron god to do with snow?" demanded Artos Flint. His black beard was crusted with ice. "This is the wroth of the old gods come upon us. It is them we should appease."

"Aye," said Big Bucket Wull. "Red Rahloo means nothing here. You will only make the old gods angry. They are watching from their island." -The Sacrifice

and:

Men like to know their god is with them when they go to battle.”

“Not all your men worship the same god.”

“I am aware of this. I am not the fool my brother was.” -TWOW, Theon I

Discussion with Wull/Flint

While we don't know what exactly will take place in these discussions, we know that as I mentioned earlier, the northerners want Theon dead:

Sire,” he announced, “the maester is without. And Lord Arnolf sends word that he would be most pleased to break his fast with you.”

“The son as well?”

“And the grandsons. Lord Wull seeks audience as well. He wants—”

“I know what he wants.” The king indicated Theon. “Him. Wull wants him dead. Flint, Norrey… all of them will want him dead. For the boys he slew. Vengeance for their precious Ned.”

“Will you oblige them?”

“Just now, the turncloak is more use to me alive. He has knowledge we may need. -TWOW, Theon I

and:

If it please Your Grace, though, the men are growing anxious. There are hundreds of them gathered around the tower, wondering what’s happened. Talk of treason is on every lip. No one knows who to trust, or who might be arrested next**. The northmen especially—”**

“I need to talk with them. Is Wull still waiting?”

“Him and Artos Flint. Will you see them?”

“Shortly. The kraken first.” -Theon I

and so when they talk with Stannis after the chapter, I am arguing that they are going to be the third time (in some way) that Stannis will have been told to execute Theon out at the tree. The northmen are nervous (Stannis just arrested some other northmen in the Karstarks) and he will need to placate them.

Previous Times:

• #1 The Ravens

Unprompted, the ravens start to bring up the tree in TWOW, Theon I first as the place that is where the terrain is an advantage:

Yet."

"Yet," both ravens screamed in unison. Then one quorked, and the other muttered, "Tree, tree, tree." -TWOW, Theon I

and again with regards to Theon as Asha enters:

The memory left Theon writhing in his chains. "Let me down," he pleaded. "Just for a little while, then you can hang me up again." Stannis Baratheon looked up at him, but did not answer. "Tree," a raven cried. "Tree, tree, tree."

Then other bird said, "Theon," clear as day, as Asha came striding through the door. -TWOW, Theon I

• #2 Asha

Asha is the last visitor before the northmen. Instead of pleading for Theon's life, she instead wishes for him to be taken and sacrificed to the tree:

"Wise. I am sorry for your mother, but I do not spare the lives of turncloaks. This one, especially. He slew two sons of Eddard Stark. Every northman in my service would abandon me if I showed him any clemency. Your brother must die."

"Then do the deed yourself, Your Grace." The chill in Asha's voice made Theon shiver in his chains. "Take him out across the lake to the islet where the weirwood grows, and strike his head off with that sorcerous sword you bear. That is how Eddard Stark would have done it. Theon slew Lord Eddard's sons. Give him to Lord Eddard's gods. The old gods of the north. Give him to the tree." -TWOW, Theon I

• #1 and #2 in Tandem

Right after Asha says to give Theon to the Tree, the ravens chime in agreeing:

And suddenly there came a wild thumping, as the maester's ravens hopped and flapped inside their cages, their black feathers flying as they beat against the bars with loud and raucous caws. "The tree," one squawked, "the tree, the tree," whilst the second screamed only, "Theon, Theon, Theon." -TWOW, Theon I

If interested: Names Said by Ravens in the Series

Final Thoughts

With Asha and the Northmen both likely telling Stannis to do this (and the ravens reinforcing the idea) we will likely see Stannis take Theon out to the Tree to execute him. And that is where Theon's previous interactions with "the tree" aka the boy who he didn't kill:

Theon found himself wondering if he should say a prayer. Will the old gods hear me if I do? They were not his gods, had never been his gods. He was ironborn, a son of Pyke, his god was the Drowned God of the islands … but Winterfell was long leagues from the sea. It had been a lifetime since any god had heard him. He did not know who he was, or what he was, why he was still alive, why he had ever been born.

"Theon," a voice seemed to whisper.

His head snapped up. "Who said that?" All he could see were the trees and the fog that covered them. The voice had been as faint as rustling leaves, as cold as hate. A god's voice, or a ghost's. How many died the day that he took Winterfell? How many more the day he lost it? The day that Theon Greyjoy died, to be reborn as Reek. Reek, Reek, it rhymes with shriek. -ADWD, The Prince of Winterfell

and:

“The north remembers. The Red Wedding, Lady Hornwood’s fingers, the sack of Winterfell, Deepwood Motte and Torrhen’s Square, they remember all of it.” Bran and Rickon. They were only miller’s boys. -TWoW, Theon I

and:

He never wanted to do any harm to Bran or Rickon. Reek made him kill those boys, not him Reek but the other one. “I am no kinslayer,” he insisted. He told her how he bedded down with Ramsay’s bitches, warned her that Winterfell was full of ghosts. “The swords were gone. Four, I think, or five. I don’t recall. The stone kings are angry.” He was shaking by then, trembling like an autumn leaf. “The heart tree knew my name. The old gods. Theon**, I heard them whisper. There was no wind but the leaves were moving.** Theon**, they said. My name is Theon.”** -TWoW, Theon I

TLDR: Nothing really new, just reinforcement that Stannis will likely be convinced to sacrifice Theon (at least initially) to the weirwood tree at the crofter's village after this idea has been brought up by the ravens (at least to the reader), Asha and now (likely) the northerners as well.