You are allowed to walk all over the ship with a drink in your hand. Whether you can between the prior drinks & the motion of the sea is another story. :-D You wouldn't want to spill a drink.
On my last cruise I was taking drinks to a friends' cabin. Because I ordered so many drinks, the cocktail waitress actually walked to the cabin with me. In the elevator I made bad jokes about resident drunks being provided truly individual service.
You cannot however walk off the ship into a port or from port back on board with an alcoholic beverage. You must finish it or spill it out (horrors).