The presence of hair follicles in human skin appear not to disturb Terahertz (THz) transmission, but existing measurements made on human head hair show conflicting results on THz scattering. It is not known if large numbers of hair strands protruding from skin would affect THz transmission. This scenario is distinct from measuring clumps of head hair because hair strands on skin (particularly on animals) are not bound together, are oriented randomly, are mostly thinner than head hair, and have slightly varying lengths. This study presents measured THz data on excised rat skin before and after shortening/removal of hair. Results show that the THz signals before and after hair shortening/removal are similar. A mathematical model is also presented to elucidate the effects of rough surfaces on THz reflection mode spectroscopy.