There is a whole bunch of factors that would go into calculating which would cool you most efficiently. In all honesty, in practice, this question is next to impossible to answer. You are attempting to maximizing cooling, while minimizing cost.
Do you factor into account the energy spent just having the fridge running? How big is the fridge? What kind of efficiency does the fridge have? Do you honestly believe you can make an accurate measurement on your temperature decreasing after consuming a glass of water? How efficient is the air conditioning model? What kind of circulation is occurring in the room? How hot is it outside? How hot is it inside? How big is the room? The questions go on and on and on. And they would all impact the answer.
My two bits is to just do both.