This is not a moral or ethical breach per se. It depends on the circumstances, just in the same fashion as using animals for food raises many ethical concerns and can be both acceptable and unacceptable, depending on how the animals are treated. Animals have great value as beasts of burden. They were a necessity for human progress in prior generations before the advent of motorized vehicles. The need for this is much less, and much less compelling and is more done as a historical reminder and a reminiscence of the bygone era. There are some situations where horse-drawn wagons and carriages are necessary because of the terrain or the extreme isolation and cultural conditions of poverty and so on where mechanized vehicles are simply impractical and way too costly.
The use of animals in this way is acceptable provided there is basic humane treatment with regard to their care and feeding and that the workload is not excessive to put them at risk of injury and suffering unduly. Most animals do not relish work, but will adapt and take it in stride, and will come to expect this as part of their day, and so will not be harmed by being trained to serve in this way. The key is whether they are subjected to punishment and harsh treatment or neglect in some way to overwork them with insufficient food and water, so they have significant physiologic stress in addition to the physical demands. So due attention and respect need to be paid to the reality this is a living, breathing animal with a conscious awareness, with feelings and emotions as well, and simply wants fair treatment done with respect for them as living things.