100 grams of honey when metabolized will release:
15 grams of physically bound water (USDA nutrient database says 17 grams)
125 grams of carbon dioxide
51 grams of water from sugar
To answer the not-asked part of the question, the reaction requires 91 grams of oxygen (0.480 cubic meters of air at standard conditions).
At 0 C, it would require about 17 cubic meters of air to dissolve that much water. So the amount of air required to remove the water is around 35 times greater than that required to remove the carbon dioxide. Warmer air temperatures dissolve more water.
The reaction would release 304,000 calories of heat. If an overwintering hive weighs 90 pounds that would raise the temperature of the hive by 8 degrees C for every 100 grams of honey consumed.
Because all of the products of this reaction are volatile, the rate of consumption of honey could be measured by weighing the hive as long as the water wasn't freezing inside the hive.
Also, it is not necessary to remove the water by ventilation, it could also be removed by condensation. An example of this would be leaving the dog in the car on a cold day, and coming back out to find all the inside surfaces of the windows covered with condensation. The same principle could work in a bee-room during the winter. I'd probably arrange for a thin membrane that gets sun part of the day so that it could auto defrost.