Both horses and dogs can "suffer" from a condition called a "roached back". Condition may be too strong a word to describe this. What it is, is a dorsal curve in the spine, usually in the thoraco-lumbar junction. In my opinion it occurs because of a restriction in either the shoulder blades or thorax. For instance my Labrador Retriever has a roached back that I think is the result of a surgical scar in his rib cage.
The roached back takes a while to develop and prevents the animal from fully extending.
My theory is that the restriction in the thorax prevents a complete movement of the energy wave of locomotion to move through the spine. The restriction causes a reflexion in the wave which is opposite of the original wave with less amplitude. The two waves, the one coming from the movement of the rear leags and the reflected wave add and subtract from each other, causing "standing waves" in the spine. Since the spine didn't evolve to accomodate these standing waves it roaches.
If you've ever watched a horse with restricted shoulders being ridden you'll see these standing waves being reflected in the rider's arms. The unskilled riders will flap their arms in response to this like they were wings.
In response these restrictions the horse and dog will change from a walk to a trot to a canter... earlier than they would without the restriction. I'm not sure why this is.
They will also exhibit either the amphibian or reptile style walk, rather than the mammalian walk.