Jon had received some letters at the Wall, it’s likely he found out that way
We find out that Jon had received a letter from Robb that told him of Bran waking up. As this is the case it could be likely that he had received others (of course he also gets letters telling him of Eddard and Robb going off to war).
Jeor Mormont, Lord Commander of the Night's Watch, was a gruff old man with an immense bald head and a shaggy grey beard. He had a raven on his arm, and he was feeding it kernels of corn. "I am told you can read." He shook the raven off, and it flapped its wings and flew to the window, where it sat watching as Mormont drew a roll of paper from his belt and handed it to Jon. "Corn," it muttered in a raucous voice. "Corn, corn."
Jon's finger traced the outline of the direwolf in the white wax of the broken seal. He recognized Robb's hand, but the letters seemed to blur and run as he tried to read them. He realized he was crying. And then, through the tears, he found the sense in the words, and raised his head. "He woke up," he said. "The gods gave him back."
"Crippled," Mormont said. "I'm sorry, boy. Read the rest of the letter."
A Game of Thrones, Jon III
Note that whilst it may or may not be something Robb would put in a letter, Arya does ask Yoren to take a letter to him. It is plausible she’s sent others.
“I'm a girl," Arya said, exasperated. If the old man was down from the Wall, he must have come by way of Winterfell. "Do you know my brothers?" she asked excitedly. "Robb and Bran are at Winterfell, and Jon's on the Wall. Jon Snow, he's in the Night's Watch too, you must know him, he has a direwolf, a white one with red eyes. Is Jon a ranger yet? I'm Arya Stark." The old man in his smelly black clothes was looking at her oddly, but Arya could not seem to stop talking. "When you ride back to the Wall, would you bring Jon a letter if I wrote one?" She wished Jon were here right now. He'd believe her about the dungeons and the fat man with the forked beard and the wizard in the steel cap.
A Game of Thrones, Arya III