There are four basic horse speeds, a walk, a trot, a canter and a gallop. A walk does not consume as much of the horses stamina as a trot, like a trot to a canter or a canter to a gallop. In this game it doesn't matter how fast or slow the horse moves, the energy consumption is the same which is patently ridiculous.
In a nutshell, energy consumption should work according to speed.