A horse's chestnuts are the obvious hard "callouses" on the inside of the leg, often quite high up.
The chestnut is the equine equivalent of the dew claw in dogs - a vestigial toe that has migrated up the leg. They sometimes grow quite long and may have to be gently trimmed back (it's dead material like hair, so this doesn't hurt the horse, although grabbing and twisting the chestnut hard does - people sometimes use this to force a particularly recalcitrant horse to lift its head).
Interestingly, asses and zebras have chestnuts only on the front legs. The hind chestnuts are also absent on some Caspian ponies and most Banker horses and Icelandic horses, but are present in the Przewalski's horse, suggesting they have been lost by these breeds. Mules rarely have hind chestnuts.