Ok, so I feel like the answer is a multi layer of possible answers here. Can you walk around with the tumbler with alcohol in it? Yes. No one is going to know if it’s water or vodka. But if you make a dang fool of yourself and it’s alcohol from your cabin that you smuggled in, they can search you and find it and punish you for it by banning you or arresting you to your room etc.
I also probably would refrain from making drinks outside of my cabin from smuggled alcohol unless you want to be caught. Someone is always watching…
But if the OP is just asking can you, as in are you allowed to carry around an open container or do you have to be in the bar, yes you can carry around an open container.