And if not, why not? Where exactly does the model fail to apply to our equine friends?
Beginning in the late 19th century, and with increasing mechanization in the 20th century, especially following World War I in the USA and after World War II in Europe, the popularity of the internal combustion engine, and particularly the tractor, reduced the need for the draft horse. Many were sold to slaughter for horsemeat and a number of breeds went into significant decline.
The link for that is here, and for the pointer I thank Braden Anderson.