Rules vary from park to park as to where alcohol is legal and where it isn't, but in most parks, drinking is legal on campgrounds and in most public-use areas, and illegal in most parking lots, pull-outs, and park buildings.
First off, it's never a good idea to go through Central Park at night. While Central Park is an idyllic tourist attraction during the day, it is technically supposed to be closed late at night and in the early hours of the morning. The vast majority of cases of crime and violence in the park occur at night.