I have always considered such words as "high-pitched", "four-legged", "oft-stated", "first-time", "self-esteem" (struggling to come up with more common examples) single words. For example, I would call "self-esteem" a hyphenated word. But a Merriam Webster editor refers to lily-livered as two hyphenated words. In the audio at 00:24, the editor says "it's spelled as two hyphenated words". Technically, are these compound words single words or not?
Edit: added the exact source.
Best Answer
In general, unless a word is listed in a dictionary in a hyphenated form (in which case it's a hyphenated word), what you are looking at is just two words that have been hyphenated.
For instance, there is no single word as fifteen-legged:
In the first sentence, the two words are joined by a hyphen because they form a compound adjective.
Logically, if fifteen-legged were an actual word, then so too should be all of the other numerical combinations—but that's neither practical nor, ultimately, possible if expanded to every iteration. (Note, though, that two-legged, three-legged, and four-legged seem to have had enough popular usage that they've found their way into some dictionaries.)
However, high-pitched has become an actual word:
Although high-pitched is serving the same function as fifteen-legged, high-pitched is a hyphenated adjective, while the hyphen-combined words fifteen and legged form a compound adjective.