I was grooming my trainer's Appaloosa mare this week and I had to get a bucket for all the hair that came off her.
Horses shed, and they shed a lot more in the spring than the fall. They also shed more if they're kept outside rather than being stalled at night.
The reason is that in the summer, horses grow a single layer hair coat. In the winter, they grow a double coat - long outer hairs and a downy undercoat. It's that downy undercoat that creates buckets full of shed hair when you groom a horse in the spring. (We often use a rubber curry coat or a shedder to get the shed hair off the animal faster, otherwise it can cause itching under the tack).