What does it mean to dream of a white horse looking at you with red eyes?

The meaning of this specific dream depends on the emotions you felt during the dream. Often red eyes on the any animal, whether it's a horse or a wolf or dog or whatever, suggests anger or rage or even demonic possession. In that case, the white horse would symbolize something that you are very much afraid of, or a problem that is threatening to get out of control. Alternatively, red eyes can simply mean that someone's very tired or worn out. In that case the white horse might represent a hero's horse, like the cowboy who rides into town on a white horse or the knight in shining armor who writes on his white horse to rescue someone. In that case the white horse represents yourself and your efforts to be a hero and to help everybody else. But the red eyes suggest that perhaps you have worn yourself out trying to be the hero to too many people too often.