My grandson recently acquired a cutting horse for high school rodeo that has an interesting condition. When stimulated or focusing on something, the horse's muzzle deviates to the right significantly. This effect is due to paralysis of the muscles on the left side of his face, which is the result of the lack of functional nerve supply to those muscles.
These muscles are innervated by the facial nerve, which is the seventh cranial nerve. There are 12 cranial nerves in all, and they're referred to as cranial nerves because they emanate from the base of the brain and exit the cranial vault through foramina (small holes in the skull that nerves and blood vessels enter and exit through). Some cranial nerves are sensory nerves, such as the optic nerve for sight or the olfactory nerve for smell. The facial nerve is mainly a motor nerve, activating muscles of the face. It exits the skull just under the ear and courses down the side of the jaw, giving off branches to various muscles.
The history on this horse is that, when he was a yearling, he suffered trauma to the left side of his face that effectively severed the facial nerve, after apparently having a run-in with a fence. I have also seen cases of this nature caused by trauma from the halter when a horse pulled back severely or got kicked in the side of the face. Some of these cases can be temporary due to inflammation and swelling, but if the nerve is severed, the condition is permanent. This horse is totally functional for his intended use. If he was a Thoroughbred racehorse, I doubt he would have been functional due to interference with maximum airflow through the nostrils.
In people, there is a condition referred to as "Bells Palsy," which is the result of facial nerve dysfunction. The condition is usually temporary and thought to be the result of inflammation from a viral infection. People with this condition are often treated with prednisone, which is a cortisone-type drug, and possibly an antiviral drug. Should a horse incur trauma to the facial nerve with clinical loss of tone to the facial muscles, I advise a course of corticosteroid medication to try and relieve the inflammation and restore function. However, as I've mentioned earlier, if the nerve is functionally transected, no treatment will restore function.