I don't have a detailed source on hand for the slaughtering operations specifically, but this is a good overview article of where the meat went:

https://priceonomics.com/when-americans-ate-horse-meat/

Just to be clear for everyone who doesn't click through. The car was one (and seemingly a very small one) amongst many reasons people ate horses, coupled with varying economic recessions, shortages of other meat, and changing consumer taste.

Yeah, over 40 years it would be easy to reduce the number of horses simply by attrition.