Jack Woltz (played by John Marley) is a big-shot movie producer. He's also kind of prejudiced against Italians, spitting out derogatory terms like "guinea" when Tom Hagen tries to make a deal with him. Of course, this prejudice might be due to the fact that he lost a young female protégé to Johnny Fontane, the Godfather's Sinatra-like godson.
Now, he's refusing to let Fontane have a part in a movie that would be perfect for him and would make him into a big star. Does this work as revenge? Sure. But most people would say it's kinda petty.
Yet Woltz has a weakness: the thing he loves. (Isn't that always the weakness?) In his case, it's a prize horse named Khartoum. In one of The Godfather's most iconic scenes, Woltz wakes up to discover Khartoum's severed head in his bed. He screams. A lot.
The horse's head is a message from the Godfather: If you don't listen to reason, this is what happens. It's not fair play, but you can probably sense the appeal—especially since, later on in the film, it's implied that this tactic worked (Johnny is in the Godfather's debt and obliges Michael's wishes during the Vegas scene).