When considering equines, perhaps one of the more interesting things to note is the development of the hooves as it obviously represents a shift from an environment with heavy foilage to a far more sparse one.
In the previous environment the equine would likely have been able to find food off of the floor and its former paw-like limbs would have helped with this, the smaller size would also have enabled it to pass undetected.
As horses evolved they became suited to a far sparser environment (plains, savanna, valleys) by becoming taller (so as to observe predators from a distance), ditching the paws for hooves (more suited to maintaining velocity and speed over a long distance to outpace predators), building up bulk and muscle in the hind legs so as provide good acceleration and changes in the teeth so as to allow consumption of grass instead of leaves.
What prompts these changes is a form of 'survival of the fittest' - the proto-horses most suited to the new plains environment would have survived and passed on their traits to the next generation whereas those who were unsuccesful would die. This would then go on for a few million years until the changes have 'added up' so to speak, and produced the modern day horse.