I always get excited about contemporary adaptations of little known traditional survival techniques (sleeping over smoldering peat, igloos, sleeping under duff piles, etc.), but I think it might turn out that a down tent couldn't compete with a shared sleeping bag or quilt in terms of weight.
One of the reasons that mummy bags are warmer per unit loft than rectangular bags is that they have less surface area. A small, spherical bag that required the sleeper to be curled up in a ball would be even warmer. Like a CPU cooler with fins or a car radiator, the more surface area there is, the more rapidly heat can be exchanged.
The reindeer hide tents in siberia probably weigh several hundred pounds. A down tent with a given loft would not only be less warm than a shared quilt with the same loft, but also much heavier (it would require a lot more down and fabric). I don't think heating of the tent by exhaled air could compensate for losses through the insulation. It could be a fun experiment, though, for trips that don't demand the lightest gear.