When you dream of part horse part man, it may represent a feeling of duality within yourself. The horse may symbolize your animal instincts and passions, while the man may represent your rational mind. Alternatively, the creature may symbolize a mixture of strength and grace.
In Greek mythology, centaurs are the most well-known half man, half horse creatures. They are known for their wild nature and love of wine and revelry. In dreams, however, they may symbolize a struggle between your rational self and your emotional impulses.
The Half Horse, Half Man creature in the Philip Jose Farmer World of Tiers series is a creature called a Kentauroi. In the Fablehaven book series, there is a variation on the centaur called an Alcetaur. The Alcetaur has a moose body and a human head and torso. These creatures can be seen in the woods of Grunhold in Fablehaven. Like the centaur, they are wild and untamed, but are also highly intelligent. They use their brains to survive in the jungle, but they also rely on their brute strength and agility.