What are symptoms of eating bad hay in a horse?

Heaves (COPD), guttural pouch mycosis, colic, potentially- death.

Colic. Colic is just a general term for abdominal discomfort in horses-human babies also colic. You may see your horse bobbing his head up and down or kick, roll and crib if it is colic, which is his way of showing you he's in pain or his stomach is upset. Or he might just act abnormally still with his ears back and his head down low, as if he were depressed. Horses' stomachs are more sensitive than most people think. Changes in diet, stress, and dehydration contribute to colic as well.
If the hay is bad because it has been damped by rain water, the moist may lead to fungal growth. Better watch that! You don't want your horse eating fungi.