From Amtrak's website:
Private stock
You may bring aboard your own private stock of alcoholic beverages subject to the following limitations:
You may consume private stock alcoholic beverages only in Sleeping Car accommodations for which you have a valid ticket.
You may not consume private stock alcoholic beverages in any public areas.
This is not to say that people haven't ignored the rules in the past. And if you're careful, discreet, and don't appear drunk you may well get away with it. But if you are caught, the conductor may do anything from simply giving you a warning, to forcing you to dump your stash, to removing you at the next stop.
Although generally the last choice is reserved for those who are 1) totally out of control, and 2) continue to drink even after they've been warned. But the conductor is lord and master of the train and he/she does have the right to kick you off without appeal.