His clan, the Battle-Borns, are known supporters of the Empire. He can be seen around Belethor's General Goods. Perhaps, out of his relationship with Olfina Gray-Mane, he seems unimpressed with the civil war. He is implied to be a bit of a romantic (or at least less of a traditional Nordic warrior) compared to the rest of the family, both in his appreciation of Nordic culture and his disdain for the war-oriented Nordic mindset. He seem to despise Mikael because of his wrong use of his bard knowledge saying that he only sing for the money and for the women.
Jon Battle-Born is romantically involved with Olfina Gray-Mane, this can be seen by pickpocketing the "letter from Olfina" from him. The story is likely to be allusion to the Romeo and Juliet story.
Jon can be used in the quest Missing in Action to acquire the Imperial Missive directing the player to Thorald Gray-Mane. However, you need to pickpocket the letter above and confront him to utilize this.
Sometimes when talking to his sister at the Battle-Born Farm, she will say that he wishes to join the Bards College as a short response. However, speaking to her again, she says that he wished to join the Bards College before he died, although she never mentioned this in her response a few seconds ago, meaning that Jon had died in those 2 or 3 seconds.