Of course, I recognize that the conventional wisdom is not exactly correct. What is likely going on is that air is being warmed by the cluster, and as a result, there is a continual flow of air from below the cluster, moving up around the cluster, and then up toward the top of the hive. As a result of this flow, colder air is being drawn into the flow from the sides of the cluster, so conduction losses through the air do not make it to the sides of the hive at the level of the cluster. However, the cluster radiates heat, pretty much as a black body. In addition, heat is conducted through the frames and combs which pass through the cluster.
In fact, I think it is Rusty Burlew over at honeybeesuite who has a fancy thermal camera that can "see" the location of the cluster through the hive walls.
However, if the cluster is touching or near a wall, as it must be at some times of the winter, then it will lose a lot more heat through that wall.
I haven't seen any quantitative information on how much water the bees need in order to liquify their food. While the water from burning honey to heat the hive will likely be in the vapor state, exhaled during respiration, it will likely condense to some extent somewhere in the hive.
I hadn't thought about bees foraging for water outside of the hive in the winter. A lot probably depends on local conditions, and also on the bees. I will have to watch the bees next time they are out to see if that is what they are doing.
This winter I have three colonies wintering in 6-frame hives. I insulated those hives in the narrow direction, since it seemed to me they would have difficulty accessing the stores on the outer walls. Since the colonies are pretty big, I suspect when the cluster is loose it touches both side walls. When I peeked at one on a 30F (-1C) evening, the cluster was at the bottom, and clearly filled the 5 frame gaps to the bottom. Couldn't see up the outside to see if they were there too. What I have noticed is that they are unusually active for the weather we are having. It suspect they perceive the conditions are warmer than they would without the insulation.
Most likely they are using more food, as they are more active. However, if it were really cold outside, not 35F (2C) as it was today, they would probably be using less, as they would be in the small cluster/no brood mode of winter survival.
When I actually weighed hives regularly through the winter (only did that one year, as it gets difficult) the bees used the least of stores when the weather was coldest.
I have heard there is some recent research showing colonies use less stores and are stronger in spring if the hives are insulated. I haven't found the actual research though. It would certainly be worth looking at.