I’ve heard numerous accounts that Dean Martin drank moderately, but the drunk act was just that, an act. A good one though:
“I shook hands once with Pat Boone and my whole right side sobered up.”
Touche.
And funny too. On one show he came out with his “Martini” and sang a little snippet, “I’m just breezin’ along with the breeze, 'cuz I’ve got a hole in my BVDs.”
I always thought the Rat Pack virtually invented the whole concept of the “classy” Amarican bacchanalia, and that Dino distinguished himself from his peers by wearing his inebriation on his sleeve, and by being laid-back about it to the point of horizontality.
I’ve had members of my own family who were remarkably functional drunks. I had a great uncle who I would hesitate to strike a match near, but was astonishingly composed. At evening gatherings he’d consume volumes of Scotch that would send me straight in to the stomach pump, and he could perform card tricks with the steady hand of a surgeon. It’s entirely plausible to me that Dino was one of these sorts of people, though that may not be the case. I simply don’t think his ability to hold a TV variety show together clearly demonstrates his sobriety, though.
Somebody already said Bukowski, so I’ll have to go for Hemingway. When his favorite bar got closed down in Key West, he grabbed the urinal and took it home with him, supposedly saying that he had pissed away so much of his money in the bar that he felt like he owned the urinal.
Two words: Nick Charles.
“The Thin Man”?
Well, I lack your encyclopedic knowledge of film, so I must defer to your wiser judgement. In my defense, I’d say William Powell isn’t as recognizable a name to some of us as Dean Martin.
Heh heh… I read that as “Don Martin.” I can just picture the sequence…
chhhhhsssshhhhhhh
galumpgalumpgalump
blllllllllleeeeerrrrrrcch
Two more: Nora Charles. She was no slouch in the inebriation department.
“Nicky, be a doll and mix us a drink. Make mine a double.”
You stode mine. 
I must admit, the Thin Man films’ portrayal of boozy bon vivants predated Dean Martin’s schtick by a few decades, and probably were quite a bit more iconic in their day than I appreciate.
Perhaps Dino reinvented the character?
Haray Caray.