It’s just a poorly worded question that slipped by anyone who should have known better.
If you have a given quantity of water, and heat it up, its mass (and thus weight) will indeed increase, albeit by an amount so incredibly minuscule that it couldn’t be measured. On the other hand, if you have a given volume of cold water, and the same volume of hot water, the hot water will be lighter by a significant and measurable amount. Given that a question about the weight of a substance must implicitly or explicitly include some sense of the quantity of substance, and given that volume is a much more common way of measuring amounts, especially of water, than count of molecules is, and given that the difference due to density is much more significant than the difference due to relativistic effects, I think it’s safe to say that “cold water is heavier” is the clear correct answer.
This refers to the properties of liquids that can be cooled below their normal freezing points (at a particular pressure) without changing into the solid state. For instance. The water remains as liquid until a nucleation site for the crystal is found. However, this typically occurs in extremely pure substances and under very static conditions, and doesn’t seem very likely to occur “in the wild” with a lake or ocean.
Yeah, duh.
I’m not sure what islider meant by it.
I agree. It’s kind of like asking, “Which is more expensive: beans or rice?” An assumption is being made.
OK, that makes sense.
I agree that the most reasonable assumptions will yield that cold water is heavier, for the most intuitive reading of the question. I still think that anyone would have some wiggle room though in a debate, as long as their reasoning was sound. I still hold that it’s really annoying that the card doesn’t specify amount vs volume though.
I don’t play much trivial pursuit but in my opinion, questions should be worded in such a way that only one possible correct answer exists, without having to make any assumptions.
I assume you’re talking about density not weight or mass.
Water is at maximum density around 4 degrees C (approx. 39 degrees F) and is less dense at temperatures above or below that point.
I always used to ask my classes “which is heavier, milk or cream?” They invariably answered cream. I the asked them why cream floats on milk if it’s heavier-
“But” they said, “the carton says HEAVY whipping cream!”
Therefore, in some common uses, heavier means higher viscosity. Since hotter water is less viscous than cold water, I’d still say cold water is heavier than hot water. 
It seems to me that the most reasonable interpretation of the question is “If you fill a container with cold water from your kitchen sink, will it weigh less or more than if you had filled the same container with hot water from your kitchen sink?” and the correct answer is cold water weighs about 1% more, which might be difficult to measure.
IRL, it’s quite likely that 1% would be smaller than the accuracy of the scale you’re using and the person filling the container might not consistently fill it the same way both times.
Why not? Just get the volumetric pipet out of the cupboard.
To be fair, we don’t know the wording of the question on the card (I guess the question as stated in the thread title is paraphrased by the OP).
But it is quite impossible to formulate a question that does not rely on any assumptions. Such a question would have to specify whether both the hot and cold water were pure or salt, whether they have the same proportion of hydrogen-1 and hydrogen-2 isotopes, whether they were measured at the same conditions of atmospheric pressure, local gravity, and so on to infinity.