You should have at least as many barrels of wine as you have dwarves. So no, you don't have enough.
To fix this, start by making sure that your dwarves aren't wasting barrels on storing things that don't need to be stores in barrels. Split your food stockpile, have one stockpile that only takes booze and another that takes everything but booze. Set the maximum barrels to zero on the stockpile that takes all the non-booze food. This will reserve the barrels for booze.
Build more farms and plant plump helmets. Make some more still and set them to nonstop production. You can enable farming and brewing on any dwarf, although the more skilled dwarves will grow more plump helmets per farm tile and brew booze faster, so it's better to have a few very skilled farmers and brewers than a lot of unskilled ones.
This thread is relevant to my gaming education.
When you say, "making sure that your dwarves aren't wasting barrels on storing things that don't need to be stores in barrels", is that something I check to see if they're doing now? Or something I just set up so that they don't do that in the future? Related: is checking to see if they store things in barrels just (k) - mouse over barrel - see what the barrel is called / what it has in it? Or is there some sort of menu where I can check this sort of thing all at once?
What is a reasonable size of storeroom? IE, is 10x8 small, reasonable, large? Should I plan to make a giant room to store all the full barrels in? (Sort of related: When I have my craftdwarfshop set to make rock pot (repeat), where are those pots getting stored? In a specific store room where they take up one space, until a brewer comes and gets them? Or do they disappear into the ether until a brewer wants them? Is this something I should think about having a specific stockpile for?)
If I have make rock pots on repeat, and I have a still that is brewing on repeat, and my booze stockpile gets full... does that even happen, the stockpile getting full (such to the point where the brewer would stop brewing because he has no place to put what he's made? Sometimes my Z menu has said that I have Drink 350 (back when I had ~60 dwarves). Is that a lot?
I have a plot growing plump helmets year round and another plot growing cave wheat whenever that's allowed, and... something else the rest of the time. How do I know if more than one type of booze is getting brewed?
When a dwarf gets a barrel of booze (since someone here said one barrel per dwarf), and drinks the booze, what happens to the container? Do I have empty rock pots that are getting recycled and then filled with more new booze?
(Am I showing my newb quotient?)