How about replacing the horses with bio- fuelled or (renewable) electric transport? It doesn't have to be much like a present- day car: if we limit ourselves to horse- type performance, the engine could be very small indeed, and could be made to last several generations, the 'car' itself being renewed and/ or replaced. The bodywork and chassis made of renewables (wood, fibre board, wickerwork, leather etc.). Slow, so no need for powerful brakes or too much safety equipment. Just a horseless carriage. Less likely to bolt or bite. Not as smelly. Can be left a few days without food.

If the fuel is alcohol, we could also reduce the human reproduction rate drastically.