I would think that a great weakness of card-based games is that you can't pretend to drop the dice on the floor and knock the table over when you bend down to pick them up...
Moving right along, wouldn't it be easier to play a card-based game while imbibing? You never know where those pesky dice are going to scatter to, unless you've invested in a dice rolling tower.
Dominoes and Mah-jong don't use dice, but you can clack the tiles down to prove a point, and the tiles won't get messed up if you spill your drink on them.
On a more serious note, there's a YouTube video somewhere by that Italian game reviewer that covers Snow in a fair amount of detail. If you haven't seen it yet you might try looking for it. I watched enough of it to get a sense of what the game play is like, and it looked very appealing.
The original version of Kingmaker didn't use dice to resolve battles. Battles were noisy and gleeful affairs, and rarely resolved sober.
And never forget that the Spartans and the Vikings both believed that every important issue needed to be considered drunk and sober. And you only act on something if your soused and sober opinions are in agreement. They did their sober and drunken deliberating in different orders, however, and I can't remember who did which first.