If questioned, Sam would doubtless tell them the truth, but Jon could not imagine him braving the guards in front of the King's Tower to wake Mormont from sleep.
When Jon did not appear to fetch the Old Bear's breakfast from the kitchen, they'd look in his cell and find Longclaw on the bed. It had been hard to abandon it, but Jon was not so lost to honor as to take it with him. Even Jorah Mormont had not done that, when he fled in disgrace. Doubtless Lord Mormont would find someone more worthy of the blade. Jon felt bad when he thought of the old man. He knew his desertion would be salt in the still-raw wound of his son's disgrace. That seemed a poor way to repay him for his trust, but it couldn't be helped. No matter what he did, Jon felt as though he were betraying someone.
Even now, he did not know if he was doing the honorable thing. The southron had it easier. They had their septons to talk to, someone to tell them the gods' will and help sort out right from wrong. But the Starks worshiped the old gods, the nameless gods, and if the heart trees heard, they did not speak.
When the last lights of Castle Black vanished behind him, Jon slowed his mare to a walk. He had a long journey ahead and only the one horse to see him through. There were holdfasts and farming villages along the road south where he might be able to trade the mare for a fresh mount when he needed one, but not if she were injured or blown.