Is it possible? Maybe. Is it plausible? Not really

In my answer about domesticating hippos I mentioned the experiments to domesticate the Russian Red Fox. After 20 generations, their domestication percentage was only 35%.

Horses have a 25-30 year lifespan, are sexually mature at 18 months, but generally don't start foaling until 2 years. by 18 years the eggs produce regular birth defects. For convenience, let's say that a "horse generation" is about 10 years.

So, after 200 years of working diligently to domesticate horses, you'd more-or-less get a 35% success rate. And that's only if you're sedentary (thanks @AlbertoYagos), focused, organized, keeping records, making observations, etc. — none of which stone-age people weren't wont to do.

Thus, it's possible, maybe, but not plausible. People simply hadn't developed culturally enough to develop the basic skills needed to do this.

Is it possible? Maybe. Is it plausible? Not really

In my answer about domesticating hippos I mentioned the experiments to domesticate the Russian Red Fox. After 20 generations, their domestication percentage was only 35%.

Horses have a 25-30 year lifespan, are sexually mature at 18 months, but generally don't start foaling until 2 years. By 18 years the eggs produce regular birth defects. For convenience, let's say that a "horse generation" is about 10 years.

So, after 200 years of working diligently to domesticate horses, you'd more or less get a 35% success rate. And that's only if you're sedentary (thanks @AlbertoYagos), focused, organized, keeping records, making observations, etc. — none of which stone-age people were wont to do.

Thus, it's possible, maybe, but not plausible. People simply hadn't developed culturally enough to develop the basic skills needed to do this.