Answer
Around each hair follicle are dendrites of neurons. These nerve cells constitute a sensory hair root plexus that is sensitive to pain and touch. When the hair is plucked impulses are generated and pain is felt.
Work Step by Step
In the epidermis, there are many sensory cells for pain, touch, and pressure--Merkel's cells, Pacinian corpuscles Meissner's corpuscles and Riffini,s cells. However, the the sensory nerve endings are mainly in the stratum granulosum, and are not very close to the surface. Since a hair cut is by definition very superficial, any pain impulse it is able to generate must be minimal or imperceptible.
