I integrate my chicks with the flock asap. I have all generations running together, and i really like it that way. You have a little more cold to deal with, so you'll have to adjust for that.
But here's what i do. Once the chicks are feathered out enough to be safe in the coop, i put them in a wire cage inside the coop. The adults free range full time, so my run doesn't get much use anymore. So i use it for the chicks. I let the chicks run the run while the adults free range. This works out great. I have tried letting the little ones free range at many different ages, and i am most comfortable with about 8 weeks - not so much because of danger from the adults. They really don't bother the babies at all. But i have found that i lose a lot of babies if they free range earlier than that....to predators, to exhaustion, to not realizing if they have cocci or digestive problems that i'm not noticing. Keeping them confined, but still exposed to the soil is the best of both worlds. I think that what i do might not work if i didn't have as much space, so you have to adjust for that.
As to broodies, i think it depends a lot on the broodies. I have gotten to where i do the same thing with the broody mama and babies, until the babies get feathered out. My broodies brood very well, but sometimes when it rains or if they have too many to keep track of, they let the babies fend for themselves, and then i have losses. I will put the broody and babies in the run during the day - and then back in the coop at night, no cage needed inside. I play that situation by ear some, and i try to observe how well they're doing and when i need to intervene in raising the chicks.