Robb returned to the quaint shop in the winter town with the younger Jon and Bran in tow, he called out to his father.
"Father I have gathered some of the household staff and Theon to accompany us to the deserter's execution. We are awaiting your orders." Ned was proud of his young heir for taking the initiative and it soothed his mind that Winterfell would be well cared for after his own time under Robb.
He wished Jon and Arya farewell and started on the road to Winterfell, intent on picking up Ice and mete out justice to the deserter. The group started their brisk ride to the godswood via the Kingsroad to the meadow where the deserter was awaiting his fate. The sky was suddenly overcast, Winterfell will probably have a small bout of summer snow tonight. Summer snows in the North are a common enough occurrence that there was no immediate cause for concern, nonetheless the whole party hastened their horses and reached the small clearing in a short while.
The outriders who initially caught the deserter brought him in front of Ned. When Ned first set eyes on the clearly distressed and dishevelled man he was overcome by a surge of pity. In his other life, he dismissed this man's true words as ramblings of a madman and that brought ruin upon the North. But inspite of his pity, he could not stop this execution.He was the Warden of the North, and Lord of House Stark and Starks always did their duty.
Before sentencing the deserter, Ned allowed him to defend his actions. The crazed-looking man looked up at Ned and with astounding clarity he realized he was living his last moments, he simply said that he saw the white walkers and he knows he is a deserter and he should have gone back to the Night's Watch and warned them.
He said, " Tell my family, I am no coward." 
Ned knew the truth of these matters but he was Eddard Stark, he had to uphold their traditions in accordance with his position. The snow had already started falling and wind was howling by then as if the Old Gods themselves were against this grave injustice. He thought of Bran and wanted to go back to Winterfell before the snows came. There was my ne possible way this sentencing could go. The Westerosi law was quite clear and succinct. The man had to be sentenced to death. He swiftly beckoned Theon who was holding Ice, to come forward. He took out his greatsword, from its wolfish scabbard. He pronounced his judgment.
"In the name of the King of the Seven Kingdoms, the Protector of the Realm; I, Eddard Stark, Lord of Winterfell and Warden of the North, sentence you to die".
He swung his greatsword and at that moment a sudden blizzard came and the scene was engulfed in a chaotic flurry, everyone lost visibility and rushed to find shelter. As suddenly as it came, the abrupt blizzard cleared and the skies returned to the normal, if slightly overcast version,in just a few moments. The gathered party was greeted by a gory sight of the beheaded beheaded corpse. Eddard thought to himself
"The Gods must be furious with me."
Nonetheless, in his usual stoic manner, he went to Bran and asked "You understand why I did it?"
Bran replied, "Jon said he was a deserter."
Ned probed further "But you understand why I had to kill him."
Bran understood what he was being asked about. "Our way is the old way" he said.
Ned reiterated their traditions "The man who passes the sentence should swing the sword."
Bran nodded, but his curiosity got the best of him and he asked his Lord Father "Is it true he saw the White Walkers?"
Ned thought that his son had an impressive insight into people as he could accurately guess that the deserter was not lying. But he still thought Bran was too young and tried to reassure his young son who had just witnessed a death for the first time. He tried to be cautious not to inspire too much curiosity in the realm of ancient legends.
"The White Walkers have been gone for thousands of years." he said.
Bran was too keen and he wasn't convinced, he pressed, 
"So he was lying?" 
Ned thought he should continue to dissuade thoughts about white walkers from Bran's mind, he was the most eager listener of Old Nan's stories afterall and said dismissively "A madman sees what he sees." but he thought he should do better and added
"But even a madman can sometimes be a messenger for the Gods, I will write to the Lord Commander Mormont informing him of the deserter's demise and request an investigation into this matter." Bran looked reassured, and Ned called out to the group.
" We must make haste back to Winterfell, lest we suffer another bizarre blizzard". He called out to two young servants to prepare the body to be sent back to his village near Lord Mallister's keep.
On the ride back to Winterfell their retinue was blocked by a corpse of a humongous dead stag, it was missing a part of its antlers and it seemed to be a fresh kill. Ser Jory was at the helm and he stopped to inspect. 
"My Lord, this stag was seemingly killed by some monstrous beast, from the teeth and claw marks it seems to be a big wolf, maybe even a direwolf, the trail seems to suggest the beast was hurt as well," he said to Ned.
"There are no direwolves on this side of the wall anymore" Ned reminded him. However, direwolves were the sigil of House Stark and he was seemingly compelled by the Old Gods to search for it.
Dismounting from his horse, he followed the trail of blood to a nearby refuge hidden slightly by surrounding trees he found the living embodiment of their house lying dead surrounded by five of its pups mewling and yipping at their dead mother.