Because Hylians have so many apple trees, I figure they probably make a lot of ciders, but they'd also make meed from honey.
Not a lot grows in Hebra beyond Tabantha wheat, so Rito make a lot of hops drinks like beer and ale. Their ale is so weak that Hylians and Gerudo allow children to drink Rito Ale as a soft drink. But they make stronger drinks to trade with other nations even if they don't drink it themselves.
The Sheika have rice paddies, so they probably produce sake from rice. They're also relatively science forward though so I imagine they also have a range of weird drinks made from all sorts of things from roots to tree bark.
The Zora make their weird jellyfish poison drink, but I imagine for trade purposes they also make a lot of wines and things with the abundance of fresh produce that grows around the wet region.
The Gerudo definitely favour sweeter based drinks. They probably produce things like Rum and Vodka to make cocktails with, I bet voltfruit can be utilized like a starchy potato or the sugars used in a similar way to sugarcane.
Then the Gorons - nothing much grows on death mountain. But they can probably dig up roots from deep under the ground and use them to make cassava beers.
