The dawn of the Automobile Age made a lot of people wonder what would come of the horse. In the year 1900 author John Elfreth Watkins even predicted the complete eradication of all animals, aside from the few that we might keep in zoos. Some thought a new era of machines would quickly make animal labor inferior and therefore animals would have to justify their existence, continuously proving their worth so that humans wouldn't just wipe them out as our own population swelled.
This cartoon by Albert Levering appeared in a 1905 issue of Life magazine and imagines the lap-dog sized horse of a thousand years hence. It seems the artist may have been on to something, as one way animals seem to prove their worth is through being overwhelmingly adorable. Squee, etc.
This cartoon can also be found in the book Predictions.