A lot of this is a moot point if "winter bees" have not been produced by this queen. These bees are fed well as larvae, and do not have to forage nor feed younger sisters. For us in OH, at least NE OH, the bees that are alive in the hive after Jan are the capped brood that emerged last, when their older sisters could still forage. So the youngest were "preserved" for overwintering.
I am not familiar with supercedure swarms. Supercedure has been pretty invisible for me - the mother queen slows her egg laying, a few queen cells mature, a daughter returns mated... sometimes mother and daughter lay in the same hive for a while. If you caught a second swarm, and the queen is laying now, that means that she was a virgin when caught, then got mated by some miracle since she emerged and you saw eggs. Or... this could be absconding. Meaning there is no laying queen left in the hive this swarm came from. Meaning something is wrong with the original hive, like a high varroa load or too much ventilation. That's a different issue entirely...
First step I would take is to get a laying queen back into the original hive. Is that an option? Or is there a laying queen in the original hive too? I say that because the advice is to take your losses in the fall, not the winter.
But again.... missing the key point to overwintering... which is winter bees emerging. Which is capped brood being produced in large enough quantity by a queen somewhere between early Sept and now.
If you can add capped brood, from a hive that has many bars, then you might be able to save this hive. But should you?
If a hive is swarming now, it has instincts to swarm when it is not swarm season. This is not something you want in your apiary. The comb is a good asset, so these bees will have left a legacy... but some hives cannot be saved this time of year, even if they are indoors in an observation hive, or outdoors and heated to some degree.
Oh and someone mentioned a shed.... People who overwinter indoors in specially constructed buildings aim for a temp of 40. Above that, the bees will try to fly. They may waste a lot of energy that way, may lose workers to "foraging accidents". A shed that will rise to about 45 when outdoors is cooler is a potential trap for bees who can exit to the outside. Oh, and they will find a way out for certain - they will find any crack that light comes in through, and it may make the shed difficult for the resident humans to use.
Yes to insulation, assuming saving this queen is the goal, that can only help. A thermostat and thermometer to check that the "heated" interior only gets to 40, that could help. Good luck.... keep us posted...