Horses are associated both with the sun in that they pull the chariots of sun gods, and with the moon in that they are seen in ocean waves which are subject to tides. They denote power and strength, as well as freedom. Because they can learn to communicate with humans (especially humans who attempt to understand them), in a dream they can represent enormous power available to our control. The horse enabled long-distance travel before the advent of modern transportation, and so is associated with travel and journeys. We still measure engine power according to “horse power,” and so a horse in a dream is a symbol of both a standard of measure and an antiquated way of thinking still in use.
When I dream of riding horses I have similar associations to bicycle dreams, in that there’s a certain balance and elegance to the mode of transportation. With horses, however, there’s also the fact that the steed is sentient and has its own wisdom.
Our expression “get back on the horse” means to attempt something difficult after failing at it previously. In that sense, the horse is an unpredictable challenge that might throw the rider to the ground or carry her where she wants to go.
Horses can be associated with demonic energy, as in the Four Horsemen of the Apocalypse, or the horse sculpture at Denver International Airport which killed its creator. http://www.denverpost.com/ci_8961169 Yet they can also be gentle and sweet. The paradoxical associations show how deeply ingrained in our collective psyche the image of the horse is.