The horse is somewhat unusual in symbology because it can have nearly opposite meaning depending on the color and activities it is involved in.  White, gold, or fiery horses are solar symbols and represent life but darker colored horses and those associated with sea gods are lunar and death symbols.  Horses can also symbolize light, power, wisdom, virility or nobility.  A winged horse is also symbolic of the sun, Light, or the cosmos. 
     In Buddhism, horses symbolize the indestructible, the immortal, or the hidden nature of things.  Buddha left home riding a white horse.  In China, when a horse is depicted with a dragon, the dragon represents heaven and the horse represents earth.  Also in China, a winged horse carries the book of law on it's back and is a symbol of good fortune.  
    In Christianity, the horse can symbolize the sun, light, courage, and generosity.  The most famous horses in the Bible are the four ridden by the Horseman of the Apocalypse and I have already covered the specifics on their symbology.  In Hindu mythology, Vishnu will incarnate as a white horse in his tenth incarnation.  For Native Americans, a horse symbolizes the combination of earthly grounding with the spirit wind and wisdom.
    In ancient societies, we find the horse strangely missing from Egyptian symbology and mythology.  In Greece, a white horse drew the solar chariot.  Also in Greek mythology, the winged horse Pegasus represents the passage from one plane to another, specifically, from the material to the spiritual.  
    In dream symbology, our term nightmare comes from the German nachtmare meaning to dream of a mare which they considered a bad omen.  Carl Jung felt the horse represented the intuitive side of man.  Seeing yourself riding a horse in a dream generally means your project or plan will be successful but, if you fall off the horse, it will not succeed.