i.e., a half-horse, half-person, along the lines of a faun or satyr. The hind-quarters of a horse and a human abdomen, chest, shoulders, arms, and head.
Does this mythological form have a specific name?
Can’t say that I’ve ever seen such a form in Greek or Roman art.
Both “cynocephalus” (a man with a dog’s head; St. Christopher ihttp://www.gods-and-monsters.com/cynocephalus.htmls one in some traditions) and “onocephalus” (a man with an ass’s head: Jesus is one in some traditions, though not apparently in any Christian traditions) are used. I’d suggest “hippocephalus” by analogy. “Hippocephalos” if you want it to look more Greek.
Damn you, SDMB advertisers! I screwed up the editing because the page kept freezing and crashing and ran out the time limit. Oh, well, you can figure it out.
According to Wikipedia it’s an early form of satyr.
They have horse’s tails and horse-sized penises, but I can’t recally any of them with a horse’s head.
The OP specifies human from the waist up, equine (hindquarters only) from the waist down.
Always with an erection … must be poplar with the ladies … those Greeks sure knew how to spin out mythology !!!
I love “hippocephalos” but it’s the other way around; anthrocephalos, hippo–um–back end. Is there a formation of this sort? Is there a variation on the word “centaur” that would work?
Satyr works, if nothing more specific comes up. Maybe hipposatyr?
Thank you both, and thank you everyone and all!
Hippobottomus?
Best thing I’ve heard all week! 
I love you for this and want to bear your children!
How would this creature be distinguishable from a faun or satyr? It sounds like it would be identical to a satyr to all but the closest inspection.
Mythology doesn’t generally work that way. Creatures tend to be broadly described in such a vague way that they can encompass all sorts of variation and lend themselves to the needs of the story. Think about the variation in gnomes or dragons or sphinxes for example.
It’s almost unheard of in mythology to create creatures with minute and irrelevant identifying creatures. Instead, “faun” encompasses all people with cloven feet. Minor details like whether they have horns or pointed ears or, in your example, cloven hooves, don’t stop them from being fauns. A being with horse feet and legs and no horns is a faun. A being with deer feet and legs and horns and pointed ears is a faun.
Or to put it another way, if you showed someone from ancient Greece a statue of the creature you describe, would they really be able to tell it wasn’t a faun? WOudl they really be looking that closely at the feet?
Ha!!
As others have pointed out, this is a satyr. The Greeks used the word “satyros” for creatures that had a variety of human and horse parts mashed together. Keep in mind, the Greeks were not interested in dissecting the minutae of every possible combination of hybrid animal. Rather, they started with a mythological character and then various artists depicted it in whatever way they pleased. (It’s not like they were writing a D&D book.)
Later on, the Romans started syncretizing and conflating pieces of Greek mythology with their own. They had a goat-man hybrid character that seemed like a close fit, so they arbitrarily declared that satyrs and fauns were one and the same. The Roman interpretation of the character just happens to be the one pop culture remembers better.
Brian?
A ha’pennytaur?
You had to ask didn’t you:
Frequency: Uncommon
No. Appearing: 2-8
Armor Class: 5
Move: 18"
Hit Dice: 5
% in Lair: 40%
Treasure Type: I, S, X
Damage/Attack: 2-8
Satyrs (or fauns) inhabit only sylvan woodlands. They are interested primarily only in sport - frolicking, piping, chasing wood nymphs, etc. They resent intrusion, however, and will drive away any creature which offends them. They can sometimes be lured/bribed with superior wine.
I had been under the impression that the faun/satyr, proper, was half goat, and thus something that’s half horse – but not a classical centaur – might have another name.
I’d suggest a lighter armor class and fewer hit dice, and No. Appearing 1-3, or even solitary. But…yeah!
(You may grin, but when I write fantasy fiction, I actually do use a role-playing-gaming system as background, in order to keep things regular. This helps avoid at least the worst continuity problems – like Conan fighting off twenty Hyperborians in one story, but succumbing to three Kozaki in another.)