score:3
In most areas transition was indeed gradual. They just stopped breeding them in large numbers. However there is one exception. Military horses. Main transition happened during WWI, and after the war many millions of war horses were slaughtered. https://en.wikipedia.org/wiki/Horses_in_World_War_I
http://grey-mare.co.uk/articles/general-interest/real-war-horses-remembered.shtm
Upvote:5
The transition was indeed slow: Cars were very unreliable and infrastructure did not exist for large numbers of cars for a long time. This is not just roads but also service stations, etc. Horses were used up to and including WW2 definitely in Poland but possibly also in the USA armed forces. Old horses were processed for things like glue and their meat was eaten so I think a reasonable assumption is that surplus horses were dealt with in the same way.