Simile or idiom, " hung LIKE a _____" [closed]

It's both.

It is an idiom, in the sense (all definitions are from Oxford Dictionaries Online)

A group of words established by usage as having a meaning not deducible from those of the individual words (e.g. over the moon, see the light).

Now, most of these words are used in their usual senses, and the whole "like a horse" part can be taken literally—the person who is "hung like a horse" is being directly compared to an actual equine. It's almost certainly hyperbole (exaggeration for effect), but that alone doesn't qualify the phrase as an idiom.

But hung is being used with a specific, unusual meaning. The primary definition of the verb hang is

1. Suspend or be suspended from above with the lower part dangling free.

And most of the related secondary senses also include the idea that the thing doing the hanging is suspended or dangling in some way, e.g.:

2. [with object] Kill (someone) by tying a rope attached from above around their neck and removing the support from beneath them (often used as a form of capital punishment)

3. [no object, with adverbial of place] Remain static in the air.

Based on these meanings, you would expect that someone who is "hung like a horse" would be somehow suspended in the air or strangled with a dangling rope the way a horse is suspended in the air or strangled with a dangling rope. Certainly when we say something like a "baby hangs like a monkey" we mean that the baby is gripping something above her head and supporting her weight that way, the way a monkey would.And one woman's horrifying ordeal of being trussed at hands and feet and then suspended in the air was described as being "hung like a fish".

So maybe "hung like a horse" means something like this?

(By Internet Archive Book Images [No restrictions], via Wikimedia Commons)

But that isn't at all what this expression means. In this case we don't know anything about how the comparative subjects are positioned. Instead, both horse and person have something dangling from their body (specifically, their reproductive organs): The expression "He's hung like a horse" means "he has a very large penis and/or testicles" because horses are known to have very large penises¹. It's a weird (reflexive?) use of the verb, only used in this expression (and parallel constructions like "hung like a mouse" or "hung like an elephant"), which makes it an idiom.

And once we understand the idiomatic usage of hang here we can see that the phrase is also a simile:

A figure of speech involving the comparison of one thing with another thing of a different kind, used to make a description more emphatic or vivid (e.g. as brave as a lion).

In this case, the comparison is between a man and a horse (or other non-human creature in extended usage), used to make the judgment about the size of the man's genitalia more vivid.

¹_{Per Wikipedia, the average stallion's penis "when housed within the prepuce, is 50 cm (20 in) long and 2.5 to 6 cm (0.98 to 2.36 in) in diameter with the distal end 15 to 20 cm (5.9 to 7.9 in) and when erect, increases by 3 to 4 times." So the erect penis, when measured from its base, can be well over twenty inches long.}