Most places celebrate the Feast of the Epiphany on January 6.
Are there any local, traditional drinks that exist that people have as a way celebrating this feast in a local and traditional manner?
Update: I am limiting this question to wines.
According to the wiki that you linked:
The earliest reference to Epiphany as a Christian feast was in A.D. 361, by Ammianus Marcellinus.
So, it would be pertinent to drink wines made from Italian grapes since the feast was held within the time of the Roman Empire.
More particularly, you might pick a grape variety from a list of ancient grapes from which the Romans, themselves, would have made wine.
Not that it's entirely pertinent to the Feast of Epiphany, but it is apt to say here that, you might purchase your wine here: https://www.epiphanywineco.com/ :)
As far as my quick and limited research has gone, there really isn't an 'official' wine of the feast - not really a Christian concept to have "official alcoholic beverages," imho.
As far as local traditions, the wiki you linked covers the traditions of the feast internationally but again, alcohol consumption doesn't really ever seem to be the focus...
Also, let's not forget that the Roman's would have had beer at this feast...