What was the purpose of the horse and carriage?

Food. Before it was tamed some 4,000 years ago it was an animal of prey like today's zebras or antelopes. It still shows in the way it will frighten and bolt easily as any horse rider will tell you.

After it was tamed, it was used as a beast of burden (although not as popular as the donkey) but mostly and from very early on, as a cavalry or chariot animal. Its role as a farm animal or as a common form of transport came much later.