Against the Minnesota Wild on October 24, Horton recorded his first career point with an assist on an Ivan Novoseltsev goal. Horton recorded his first career goal on November 1 against the San Jose Sharks. In the next game for the Panthers, against the Los Angeles Kings, Horton scored his second goal in as many games. On January 9, 2004, Horton became the first rookie in NHL history to record a goal on a penalty shot, scoring against Philadelphia Flyers goaltender Jeff Hackett. Three seasons later, on October 22, 2006, Penguins rookie Jordan Staal matched the feat and surpassed Horton as the youngest player to score; Staal was 183 days younger than Horton was when he scored. Four days after his penalty shot goal, Horton suffered a torn rotator cuff and labrum which could potentially have ended his season. At the time, he was third on the Panthers with ten goals. Following an examination by surgeon Tony Miniaci, Horton was told he could rehabilitate naturally and did not require surgery on his shoulder. He returned to the Panthers in early March and scored in one of his first games back against the Tampa Bay Lightning. However, his shoulder troubles continued and it was determined that surgery was ultimately required. Horton ended his rookie campaign with 14 goals and 8 assists in 55 games.