In Shakespeare's Play, Julius Caesar, The horses belonging to Caesar wept because they knew his death was drawing nigh. This was a sign, along with many others that foretold Caesar's death in the Senate.
Achilles' horse Xanthus, foretold Achilles' death. Xanthus was not a normal horse, he was an immortal horse and he spoke aloud.
|The Gray of Macha|
Thereat the Gray of Macha came and let his big round tears of blood fall on Cu Chulainn's feet. And then Cu Chulainn leaped into the chariot, and drove it suddenly southwards along the Road of Midluachar." (An Anthology of Irish Literature, vol. I, by David Greene)
In this case, I'm not sure if the Gray was foretelling the future, he may have just been aware of the circumstances. Other events foretold the death of Cu Chulainn, and the Gray could have been privy to some of them.
But why horses? I have several ideas, which are merely speculations:
Perhaps because they are man's "second" best friend. Like dogs, horses are man's companion more so than most other creatures. People bond with their dogs and horses, and this bond is celebrated in many stories.
Mythology about Cu Chulainn, and Greek mythology are steeped in omens and prophecies, so why not have the horses involved?
Additionally, animals have a keen sense of the approach of danger. Their senses are much keener then ours. A dog knows when someone is approaching before a person does. They also can supposedly sense when someone is good or bad. People can sometimes tell too. Nothing really has to happen, but certain people make us uncomfortable: it's either women's intuition (if you're a gal) or else a fine reading of body language, tone, and the eyes. There are also stories from WWII were the fighter pilots knew who wasn't coming back just before a flight. If people and animals have such keen senses, then why not exaggerate in a story and make the horses cry or talk? Mayhap these legends were born from an exaggeration of the amazing abilities of animals coupled with the horse's tendency to freak at things they perceive as threats.