Yes, the bestial Krampus is purely folkloric, and details regarding his appearance and behavior are rather amorphous. His exact appearance varies depending on time, place and available costuming materials. In fact, the more you explore the nature of Krampus, the more you come to see him as a byproduct of accumulated beliefs, traditions and primal fears.
But what if he were real? What could we say about this bipedal, cloven-hoofed monster? And what about that lolling, serpentine tongue? Let's slip on our goat-fur cryptozoologist pants and dream a little.
We might assume Krampus is a meat eater, given his often-fanged appearance and penchant for child abduction. And if human children factor into his diet, then his tongue might serve as a means to procure them. In some early-20th century postcards, we observe this prehensile appendage wrapping its way around an unruly child. Nothing in our natural world quite matches this biological adaptation, however. Iguanas, frogs and woodpeckers all use elongated tongues to snatch their prey, but Krampus' large tongue would seem to enwrap and constrict significantly larger targets.
The closest match we find in nature is the 18-20 inch (45-50 centimeter) prehensile giraffe tongue, which it coils around shoots and leaves. This might seem to suggest Krampus feeds primarily on vegetation, as is certainly more befitting of the orders Bovidae (which includes cloven-hoofed goats) and Artiodactyla (which includes even-toed ungulate giraffes).
But perhaps Krampus is something else entirely: a hoofed carnivore descended from the extinct order Mesonychid, predatory land ungulates — or a relative of the long-extinct Artiodactyla Andrewsarchus, which some paleontologists interpret as a cloven-hoofed carnivore.
Perhaps the balance is a bipedal omnivore that feasts on abundant greens in the summer and cruelly-won meat in the winter — a notion that fits well into Krampus' legacy as a monster born of winter survivalism and post-harvest anxiety.