In the specific case of horses:
An excellent source for research into equine domestication is "The Horse, the Wheel, and Language" by David W. Anthony.
His thesis is that horse domestication began in the Russian and Asian steppes, where they were first hunted as food, then held in herds for meat and milk, but that it was also here that they were first used for riding.
He has conducted numerous digs in the Russian and Asian steppes and also done modern day tests with various materials to determine, from teeth wear patterns, when and with what sort of bit horses were first ridden and/or harnessed.
DNA analysis has shown that it was quite possibly a single mutation in a stallion that would allow the animal to be ridden and that this gene was passed on to mares.
In addition, Anthony did tests with various materials available to people then and used them as bits on modern day horses. He would then compare the wear patterns with those found in grave sites or buried refuse piles that contained horse skulls. His findings show that these skulls indicate wear on the teeth that would match what had been caused by using leather, bone or wood bits. Some of the findings are disputed, but he's spent years adding to this research and it seems to be becoming accepted.
This may have happened around 4-5,000 BCE - moving original estimates of horse domestication back another 2,000 years from the original 4-4,500 year estimates.
The title of the book refers to the massive effect this increased mobility had on the spread of the Indo-European steppe people and hence the resulting dominance of Indo-European languages from Ireland to India.