--can certainly affect the face, and involvement of the face is noticed in some autoimmune and toxic causes of neuropathy (i.e., celiac, heavy metal poisoning, ciguatera, Sjogren's). It's also been reported in neuropathies due to nutrient malabsorption.

Of course, there are conditions, like trigeminal neuralgia of the face, that are, technically, types of peripheral neuropathy but are better known by other names.

In truth, any nerve damage outside the brain or spinal cord is a peripheral neuropathy, but in many situations would not be described as such, or would be given a more specific name. For instance, nerve damage due to compression--spinal radiculopathy, carpal or tarsal tunnel--are neuropathies by other names.