It's a mainly with predators that we have an easier time toilet training them. Evolution has killed off those that shat in their own caves because of diseases and bringing food back to a contaminated den will in turn contaminate the food. Whereas horses and most other herbivores live out in the open, move around more and travel long distances to graze.
I could be wrong about this but I'm fairly sure dogs have been with man for A LOT longer. Like 40,000 years ago, and I think, just from a quick Google, horses are like 4000 years...
Frank T. Hopkins: Shunka Wakan? Big dog. There's no word in Sioux for horse. When the Indians saw the first one the Spanish brought over, they didn't know what the hell it was. When they saw how it could run, carry a man through battle, become his friend for life, well, they figured it had to be a sacred animal.
"Horse meat is commonly eaten in many countries in Europe and Asia. It is not a generally available food in some English-speaking countries such as the United Kingdom, South Africa, Australia, the United States and English Canada."