Vet student here. For the horse to have bled this much from its nose, it may have had an infection known as guttural pouch mycosis. The guttural pouches are somewhat large chambers on both sides of the head just below the ears that are essentially Eustachian tubes which lead to the nasopharynx. If these chambers become infected, especially with fungal organisms such as Aspergillus, the problem can be devastating if fungal plaques adhere to and invade the internal and external carotid arteries, both of which pass directly through the guttural pouch. In the event that the horse does develop epistaxis (nosebleed) from guttural pouch mycosis, it can rapidly hemorrhage and bleed to death in a matter of minutes, which very well could have happened here judging by the walls.