As I said in my original post, "People with lots of money who are used to getting their way in all things don't intimidate easily."
I believed that then, and I believe that now.
Woltz would have been completely freaked out by the horse head, as anybody would be. After that, it would have galvanized him.
The novel provides more detail. Woltz was intimidated because:
1. The horse killer got past his security, meaning that his security was no good.
2. He boasted to Tom that he was friends with J. Edgar Hoover, the FBI director. But, what could Hoover do for him now? "What was the penalty for killing a horse?" he asked himself. Would the FBI even investigate a horse murder?
3. If that's what Corleone did as a warning, he must have something "infinitely more painful" in store if Woltz still didn't give in. You can infer that Woltz was afraid that, if there was a next time, it'd be his
coglioni that were cut off, not a horse's head.