Not really. We had a similar reduction in the global horse population at the beginning of the 1940s. We used to have basically a couple horses per person there for a few thousand years. We still have plenty of horses, most even have better lives now. Hopefully we can finally make horse racing financially unviable so we stop killing so many horses for no good reason.

There are already people who have pet cows that they won't eat when the cow dies. Those people will tend the smaller herds.