Haymitch would always drink on Christmas, as he did the rest of the year round. Drinking was just his thing, as everyone knew, and holidays just wouldn't change that fact.
Years after the war, though, a knock sounded at his door. Upon opening it, in rushed two little kids, followed by a rather worn-out looking Katniss, who told Haymitch that "He's babysitting this Christmas, or she's destroying his alcohol supply". Although he took the threat reasonably seriously, he decided he'd rather have them all destroyed than babysit the kids.
Two hours later, all his alcohol (even the secret supplies under the bench) were gone, and he was sat on the couch with two kids curled up against him as he read a remastered "Night Before Christmas".
"The Mellarks were tucked up warm in their beds,
While visions of toasted-buns danced in their heads."
From that Christmas onwards, for just that one day every year, he wouldn't drink a single drop of alcohol...
...That wasn't just because Katniss had a habit of removing every bottle from the premises on the 24th and wouldn't return it until the 26th at the earliest (Depending on if he had been a "good boy" that Christmas).