Since the "breeds" of these chickens are bred so differently by so many breeders and hatcheries, there are countless strains making generalities difficult even to speak of. With that caveat, here goes.
All your listed breeds are large fowl, heavier birds. Such birds take awhile to grow, fill out and develop. They don't "hurry" like a small frame hybrid like a sex link or a Leghorn. They are all likely to wait until somewhere around 22 weeks, which in this case means January, one of the two darkest months of the year. Sunlight is essentail for the eye to tell the brain to tell the reproductive system to function.
Barred Rocks vary from 20-25 weeks, BA are similar. NH were bred to mature a bit earlier, but I wouldn't guess before 22 weeks, while the BO will likely trail the pace at a full 25 weeks. It is also important to realize that even among the same breed, different individual birds will choose their own beginning time. You're looking at January all the way around. Maybe, just maybe, one of them will award you with a Christmas gift, but it would be a shock, really.
