"Beve un vino acido."
I'm American. Maybe that's the difference. But I cannot remember ever having heard or used any of these adjectives to describe wine. I wonder if, in Italian, ehy are referrring to some specific type of wine of which we are not aware. If they're really trying to teach us the word for "sour", it seems there would be many more logical choices for the subject of the sentence.
Are you referring to English or Italian? I can answer with regards to (American) English. You don't want to use "a" to refer to a portion of wine. You would specify the portion, as in "I have a glass of wine", or "I may drink a sip of wine", or "Please bring a bottle of wine". As f.formica says, you can speak of different types of wine using "a"; e.g., "I like a nice red wine" or "Do you want to order a Pinot Grigio (wine)?" In the latter, I would omit the word "wine" and just say the type ("a red", "a Malbec", "a Chardonnay"). You can also say "a glass of red" or "a sip of Zinfandel", etc.
For the record, I'm American and I see absolutely no problem with saying "sour wine". Now, I can't say I've heard it used before, but that doesn't make it an invalid Italian sentence. The goal is, of course, to understand it in Italian, so if you're translating it back to English in your head to figure it out, and then complaining that it doesn't sound right.... You're doing it wrong (there are occasional exceptions).