Learn Spanish (Latin America): Damas y caballeros, buenas noches.

When you are speaking directly to an audience to get their attention, you drop the definite articles (el, la, los, las). This is called direct address. If you were talking about them instead of to them, you would need the articles: las damas y los caballeros.

Why does the word for "gentlemen" (caballeros) look like it has to do with horses?

It does! Caballero comes from the word caballo (horse). Historically, it referred to a knight or a horseman. Because knights were expected to be chivalrous and polite, the word eventually evolved into the standard, formal term for "gentleman."

I thought buenas noches meant "good night". Can it also be used as a greeting?

Yes! Unlike English, which splits greetings and farewells based on the time of day ("good evening" vs. "good night"), Spanish simply uses buenas noches for both. You say it when you arrive at a formal event after dark, and you also say it when you go to bed.