I submit that this source is to be found in their grotesque effect. This will also explain the fearful and laughable appearances of the devil. In Freudian terms, the ambivalent figure is split into a fearsome and a laughable one. Figure 1 Minor devils, demons, satyrs and hobgoblins. After a wall carving at Nineveh.
Devils are just such hybrid creatures, part humans, part goats.
Not only horns, tails and hooves have been associated with the demonic, but even the very notion of the grotesque. This point deserves some consideration. Gombrich's inspiring discussion of the grotesque would strongly support both claims. To this, I would add that the relegation of the grotesque to the supernatural is an all too easy way of handling it. The grotesque creatures leave us defenseless, threatened, irrespective of the question which side of the ultimate limit they inhabit.