Answer:
In the movie, it didn't show Mickey Mouse, so you never got to see the other side of soda; the soft side. In the book it says "He may have belonged to another guy, but he was Soda's horse" this quote is talking about Mickey Mouse.
According to Ponyboy, Mickey Mouse was one "ornery pony," but Sodapop loved him for it (39). The horse would only come when Soda called him, and even though Mickey was down right mean to everybody else, he and Soda shared a bond.