You could, but it might not be the most wise decision. Although it's relatively common to see people enjoying a cold one in a park, according to the law, it's a big no-no.
Currently, drinking in places "prohibited by federal law" carries a fine of 500 to 1,500 rubles. Places prohibited by law include courtyards and stairwells of apartment buildings along with playgrounds and public parks.
As for trains, don't let Venedikt Yerofeyev's "Moscow-Petushki" fool you. While philosophizing on trains is allowed, drinking is certainly not. That goes for the metro, too, if you're a nighttime reveler.
And note that since March 2013 the sale of alcoholic drinks between 11 p.m. and 8 a.m. is prohibited throughout Russia. Buy yourself some mors instead and save yourself some trouble, and the hangover.