Overall, the more alcohol consumed, the smaller the brain volume, with abstainers having a higher brain volume than former drinkers, light drinkers (one to seven drinks per week), moderate drinkers (eight to 14 drinks per week), and heavy drinkers (14 or more drinks per week).
Men were more likely to be heavy drinkers than women. But the link between brain volume and alcohol wasn't as strong in men. For men, only those who were heavy drinkers had a smaller brain volume than those who consumed little or no alcohol.
In women, even moderate drinkers had a smaller brain volume than abstainers or former drinkers. |CNN|
Frustratingly little is said about the cognitive impact of lower brain volume. Only that, "greater amounts [of shrinkage] in some parts of the brain have been linked to dementia," which manages to raise a lot of questions without actually answering any. This study, by all appearances bona fide, seems to indicate that there is no link between brain shrinkage and cognitive function.
But here's something that google popped out when I tried to investigate the link. Brain shrinkage is also linked to B12 deficiency, and B12 deficiency is something you sometimes see in alcoholics.