"I don't have any wine."

Translation: У мене немає вина.

[ardaemre13]

As I learned, neuter singular nouns like "вино" ending letters must be -o. If it was plural, it wouldn't be -a? Or вино is plural or singular?

[skstudio]

"У мене немає" requires the genitive case, therefore "вина́."

• "Вина́" is the genitive singular form of "вино́."
• "Ви́на" is the nominative plural, accusative plural, and vocative plural form of "вино́."