I’d skip the hot water bottle (and the potential of soaked sleeping bags) and spend 60 cents each on hand warmers that will last far longer:
Those hand warmers won’t add a lot of Joules, but emotionally can help because it’ll feel like they’re warming up whichever body part they choose.
Fuel consumption, for me, in those situation? Watching every pot, not over-heating the water nor letting anything reach a boil? With lots of hot drinks, but no wasted pasta water? An ounce per person per day. If there’s snow melting, I bring a HX pot which may or may not reduce total weight over just a weekend, but if I clearly have extra fuel towards the end, then I have the luxury of a hot shower (or at least sponge bath) and unlimited hot tea (tea bags weigh nothing).
But with Scouts? All sorts of mistakes will be made. I’d bring 2-3 times as much fuel. You could have a competition to see which patrol can cook their dinner with the lowest fuel usage (weigh propane cylinders before and after), but you don’t want them scrimping on drinking water or hot chocolate so they stay hydrated.
Instead of hot water bottles, plan on warm water bottles (e.g. pee bottles). Dumpster dive at the recycling center for Gatorade and other wide-mouth plastic bottles to save 1) that frosty trip to the outhouse and 2) straining to hold it in all night long and not sleeping well. Then, after the trip, take them all back to the recycling center – only cavers’ drinking/pee bottles are bi-directional.