I think the failure of a queen mated in December, may have more to do with old drones on their last leg, not getting the job done. Drones may be mating, but the best drones in their peak, may of been passed by. Which is drastically different than the point I am making.
I have had late season queen also fail, as well as a/a queens, and a whole bunch in the middle of the summer. I think that memories of the few bad queens mated in winter, probably are best recalled in a timely manner, to bolster a particular point, when convenient enough to remember it that way. Maybe that is what is happening here.
Late season drones, or poorly raised "emergency queens", make for a crappy short laying queen. But it was not for the lack of sperm or some idea that the queen did not mate enough. If your raising queens in December, or having your bees raise queens in December, you or the bees are at fault. But it is convenient to blame it on the number of drones mating. I suspect crappy queens, or crappy drones at a bad time of the year....not due to the sole reasoning of number of partners.
I've heard many beekeepers claim a "poorly mated" queen, which they are indicating a mating with too few drones. And that is not correct. The queen may not be good, the drones could of been old or passed their prime (Old drones do not win mating wars...drones in prime do. Take away the primed drones and the lesser quality older drones are now mating)
But the point is...one good drone leaves enough sperm for a queens lifetime. And if you have a bad mated queen, whether in summer or winter, other factors are at play.