This is handwringing over the decline of paper or pencils after computers came about when paper didn't magically come about by itself. Horses were not wild animals in North America at any point in modern history and barely in other continents. They were purely bred for industry, travel, and hobby. When industry and travel no longer became a thing we stopped producing them: a clear 1-to-1 correlation.
There's already been reductions in human populations without AI from leisure, abundance, culture, etc, - a very very different causality than horses.