Why in the "old West" were places where horses were kept called livery stables does the word livery have anything to do with horses?

http://www.oldlivery.com/about/livery.htm
Livery in the Old West was essentially a parking garage or hotel for horses and sometimes other animals. In England, much earlier, livery had many other meanings.

https://en.wikipedia.org/wiki/Livery_yard#History_of_livery_stables_in_North_America
Before the automobile made them obsolete, liveries were expected in nearly every town. But there were different kinds, providing different services.

https://www.google.com/search?q=origin+of+word+%22livery%22&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&channel=fflb
How livery became associated with horses: medieval nobles provided specific colors of matching clothing to their servants. Initially "livery" referred to providing food and these clothes to your servants. This was extended to include feeding and sheltering the horses.