I am a Seventh Day Adventist, but I will say yes Jesus drank wine. Wine is spoken about as fine- blatantly obviously- in the bible, the exception being if your drunk.
At the same time though, the Bibles strong words about the effects of alcohol ("Wine is a mocker" etc) certainly suggest for you to have it in moderation.
Ideally we shouldn't drink wine at all though ourselves and we should preserve our bodies. Back then was a different time period, and wine was often a key source of their daily fluids. Today we can have fresh, healthy water.
When Jesus was on the cross he turned down alcohol to keep his mind sharp. If we drink alcohol, then we open our minds to being weakened by others and our emotions.
Wine also by many is not drunk in moderation. It would be better to ban it, because lets face it so many people lack self control. The wine itself is not needed, and it causes crime and fights, so why have it?
But that is beside the point- Jesus drank it, IMHO.