Maybe I didn`t get everything....
What would be the problem with keeping things as they are? Spoiled honey?
Agreed.... I think there is no problem leaving it on. Maybe the keeper wants to condense the size of the hive down for winter? Why, if the frames are not empty? Of course the bees heat the cluster and not the hive space. A Southern keeper here so I have no idea....
Honey is hygroscopic. It absorbs moisture. Open uncapped honey will absorb moisture from the air around it. Cold uncapped honey, absorbs even more moisture as condensation settles on it from the air around it. For example water droplets on the outside of your cold glass of choicest beverage. Honey of high moisture will ferment and spoil, thus becoming a cause of dysentry or even poisoning to the bees if and when they consume it. The hive internals is humid. Cold uncapped honey kept on the hive in presence of the humidity will spoil. Rather than the uncapped honey being a source of nourishment to the bees over the winter, it will kill them.
For these reasons you cannot store uncapped honey. It must be sealed and frozen if you want it to keep and for it to be safe for the bees later. In other words bag the frames and put in the freezer. If you can not or do not want to do that, the other options to consider have already been listed above. Pick one.
In northern climates the hives need to be condensed for winter or they will die from exposure, they will freeze. The thing to to is to take off everything they do not absolutely need and make their space (volume) optimum size and manageable for the winter. Get them down to the smallest space possible, yet a large enough space to have enough stores in it to make it to spring. The space to stores balance is the thing that is unique and regional; the difference in beekeeping from one area to another. Most everything else about the apis mellifera is universal.
Hope that and other comments added above help to sort out what you need to do.