Which disease in horses is characterized by the degeneration of the brain and spinal cord?

The disease characterized by the degeneration of the brain and spinal cord in horses is Equine Protozoal Myeloencephalitis (EPM). This condition is caused by the protozoan parasite Sarcocystis neurona, which affects the nervous system, leading to neurological signs and symptoms. These can include muscle weakness, lack of coordination, and in severe cases, seizures. The degeneration occurs as the parasite infects the brain and spinal cord, leading to inflammatory reactions and resulting in the clinical symptoms observed in affected horses.

In contrast, other diseases listed, such as equine influenza and rabies, are associated with respiratory issues and severe neurological symptoms respectively but do not specifically involve degeneration of the brain and spinal cord in the same manner. West Nile virus does impact the nervous system, but the specific mechanism and presentation differ from EPM's degeneration and inflammation. Thus, EPM is distinct in its progressive nature and direct parasitic impact on the central nervous system, making it the correct answer in this context.