Actually, they work hard to prepare their best horses for the Nadaam Festival. It is considered a disgrace to have a horse die there or at any race. Even later, if one of their race horses die, it is a disgrace, and they will try to hide the fact that it died. And if the horse is sick, they know how and will quickly end the pain. But no, they are not attached to their horses like we are. They are a source of pride and a measure of wealth, not loved and cared for as pets. But I don't think they eat them, but they do like the fermented mare's milk.
