My 3' x 6' brooder is in the coop. I've put chicks in it straight from the incubator when temperatures were below freezing. As long as you have an area in there that is warm enough they are not going to go to sleep and freeze to death on the cold side.
How are you providing heat? I use a heat lamp but several have been very successful using a heating pad cave. Many have used heat plates but some of those come with a warning to not use their heat plates in temperatures below 50 degrees Fahrenheit. It depends on the heat plate. Ohio brooders (an inverted box) can work really well too if they are set up properly.
I like having one area warm enough with other areas that cool off a lot. Some mornings my brooder has frost on the cold side but the area where the chicks are is plenty warm. I think having cold areas allows them to acclimate faster than if it were all tropical temperatu