In the comic, they were buddies from Vietnam who were as close as brothers. After the war, Storm Shadow went to Japan, and Snake Eyes came home to find his family dead (in a sorta convoluted twist that involved Cobra Commander's brother and indirectly led to the founding of Cobra), so he joined Storm Shadow in Japan. He quickly became better than SS, and the Hard Master wanted to make SE his heir. SE refused.
Cobra Commander, meanwhile, had hired Zartan to infiltrate the clan and kill SE (whom he blamed for his brother's death). Zartan found peace as an apprentice swordsmith, but CC threatened to expose him to the clan and sent Firefly in to make sure Zartan did his job. Zartan used a high-tech bow (and an arrow stolen from SS, to frame him) to home in on SE's heartbeat and shoot him through a wall, not realizing that at that moment, the Hard Master was demonstrating an imitation technique to SE by imitating his heartbeat. The Hard Master was killed by SS's arrow, and SE saw SS apparently fleeing the scene. He was actually chasing Zartan (whom he didn't know) as far as his escape vehicle, a Cobra helicopter (presumably flown by Firefly).
SS joined Cobra and made his way through the ranks to become CC's personal bodyguard, knowing that CC would know the identity of the killer. He eventually found out and snuck into the Pit to inform SE, and the two attacked Cobra Island to seek revenge on Zartan. He was gunned down by the Baroness, left for dead, and, when he came out of his trance, he went into seclusion for a while before accompanying SE on a mission or two and officially joining the Joe team.
So, short story, in the comic book, he was always an honorable sort and sought especially hard to atone for his deeds as a Cobra once he left the organization.