What does "Wine! Because you never got a pony" mean?

This is more of a question about culture than about language. There is a certain stereotype in Anglo-American culture of children, and particularly girls, having a particular affection or fondness for horses. Some explanations are covered in brief in an episode of All Things Considered, in a Kitchen Sisters segment called Why Do Girls Love Horses, Unicorns And Dolphins?.

Regardless of the level of truth in the stereotype, there does exist a genre of stories of horse-loving girls like the Woodbury Pony Club series and frequent references in popular culture, like the season 3 episode of The Simpsons, "Lisa's Pony." The reality is that although these novels make horse ownership seem accessible, it is realistic only for the very privileged (this is, in fact, the plot driver in the Simpsons episode). The vast majority of children who beg for a pony will never have one of their own— it is, indeed, the kind of childhood fantasy that most will laugh at as adults.

Wine! Because you never got a pony suggests that the one substitutes or compensates for the other. In other words, you were denied a pony as a child, but you can drink wine as an adult— to enjoy it, but also to rue your unreachable childhood dream, and therein lies the humor.

The construction of the sentence:

Wine! Because you never got a pony.

mimics the construction of other well-known advertising slogans, where the advertised product is named, followed by the slogan. The cosmetics manufacturer L'Oreal uses a slogan which is very similar to the wine meme slogan:

L'Oreal. Because you're worth it.

The meme is intended as a funny, "unofficial" advertisement for wine.

As to the meaning of the "Because you never got a pony" slogan, the implication is that when you were younger, you wanted a pony. However, your parents did not get you one, and now, as an adult, you resent that, and have resorted to drinking wine to drown your sorrows.

This is a variation on the Wine O'Clock theme: What time is it? it's always Wine O'Clock!

The basic premise of the quote is that everybody needs wine, but as cover you may need some kind of excuse, however implausible, in case a hypothetical spoil sport asks why you are having wine.

So the tongue-in-cheek potted cynical response would be, we drink because we are emotionally damaged due to a deprived childhood. The pony contrivance is shorthand for this. In other words, the person is not, heaven forbid, alcohol dependant, but deserving of sympathy, rather than judgement or intervention.

It is a joke. It is intended as a funny way to say that its time to drink wine.

The reason it is funny is because people who have had serious hardships in life sometimes turn to alcohol to cope with their troubles, but not getting a pony as a child is a silly thing to complain about and is an even sillier reason to drink wine.

"Wine. Because you never got a Lamborghini when you turned 16." This would be the male equivalent to the pony saying.