Only the eyes drift not the whole head. To be more precise, they drift to the ear with the cold water and then there is a correction reflex which reorientates them forward. This produces a jerky eye movement. The path of the reflex is from the semicircular canal in the ears (which controls balance), the 8th nerve, into the brainstem, then up the brainstem, then back out to the eye muscles. It is suppressed in awake individuals by the higher brain but the reflex reappears in unconscious people (when the higher brain isn't working). If the brainstem is not working, the reflex would not be present (however, you would be able to tell as the person would not be able to breath unaided). Some fish have that reflex as well, when you squirt cold water at their gills, they orient towards the squirt of cold water.