No Cure But Time
In theory the spell greater restoration would work, as hangovers are likely a level of exhaustion or two. As has been noted, dehydration is a large part of becoming hungover, so dying of thirst is akin to a lethal hangover. But, if there are any other side effects or aspects to being “hungover” then the spell would not technically remove those penalties. You need to break out a wish spell to be sure.
Hangovers. Even in a magical world of dragons and wizards there’s no real cure.
If alcohol’s a toxin, couldn’t you get rid of it and its effects with Neutralize Poison? Or in 5e, Lesser Restoration to fix the ‘poisoned’ condition?
In broader terms, if it deals ability damage (I know, that’s not present in 5e, but it is in 3.5/PF), or causes a status condition, can’t it be cured with the right magic?