There is no one way to do this that is right where every other way is wrong. We all do this many different ways for our own reasons.
I have no idea what you mean by "chilly". There are threads on here where a broody hen raised chicks in mostly snow with temperatures often getting well below freezing. The chicks run around eating and drinking until they get cold, then they run under Mama to warm up. The colder it is the more the risk. When it's freezing type of cold something that is an inconvenience in warm weather can soon become critical, accidents can happen any time in any conditions. But in general hens have no problems raising chicks and keeping them warm in temperatures many of us consider chilly or even cold.
Some of us grew up watching broody hens hatch eggs and raise their chicks with the flock. With me, that was a total free-range situation, a coop but no run. Hens have been doing that for thousands of years, as long as there have been chickens. They are living animals, about anything can possibly happen, but chickens are not extinct yet. There are sometimes exceptions but in general the hens do a great job taking care of their chicks. The other chickens in the flock generally do not harm the chicks, if necessary Mama will protect her babies. Usually that is not necessary, not all chickens try to attack any baby chick they see. She keeps them warm and protected from the weather as necessary. She teaches them to eat, drink, and how to be chickens. The chicks have no problems keeping up with Mama, she does not run to try to get away from them but is constantly clucking to let then know where she is. It's amazing how quickly those chicks can dart around.
Your biggest risk is predators. I don't know where you live and what actual predators are there, I suspect it's more than you listed. Around here my biggest risk to a baby chick is a snake but that is pretty rare. Dogs are a threat to the entire flock. I have owls and hawks around but hardly ever have a problems with them. Others have significant issues with birds of prey, a lot depends on your unique circumstances. I have all the usual suspects for the middle of a continent. The smaller the chick the more things can eat it. There is no way I can assess the risk you would have to predators. Somebody a half mile down the road could have a totally different result than me. It just depends on which predators happen to be at that spot.
Some people isolate a broody hen while she incubates and hatches, some people isolate a broody and her chicks when she is raising them. We each have our own experiences and reasons. Our set-ups and predator issues are unique. There are benefits, risks, and inconveniences to all of them. I can't tell you what is he right decision for you, but I can assure you the nights being a bit chilly is not a concern. The broody hen can handle that.