Horses where the plaything of the rich. Farmers were using oxen not horses for the most part. However the modern plow (invented in the mid 1830s - John Deere being the best known inventor, but others were inventing them about the same time) needed the faster speed of a horse to work well, but if the previous farming technology worked for you then oxen (or donkeys ... - there are several other work animals used in different areas for farming) were better.

There are likely more horses today than there were in 1900 - but now they are play things for the upper middle class living in the exurbs (commuting via car to their city job). Sure there are a few Amish (and other similar groups) making a living with a horse, but most of them are toys for the wealthy.

Do you have a citation for the horse number? My research [0] shows we have a 1/5 out peak number in ~1900 and our population has 5x since then. This means per capita horses in the country is down 96%, while absolute count is down 80%. Both are huge numbers.

0 - https://datapaddock.com/usda-horse-total-1850-2012/