What kind of cold temperatures are you talking about? Cold to us humans is often just getting comfortable to chickens with their down coats.
I've had chicks 5-1/2 weeks old go through nights in the mid 20's Fahrenheit with no supplemental heat. These chicks were in my grow-out coop with great ventilation up high but great wind protection down low where they were. The conditions you are moving them into can be important. My 3' x 6' brooder is in the coop. I keep one end toasty but let the far end cool down as it will. Some mornings there was ice on that far end. Since my chicks were exposed to cold weather they were acclimated. They spread out all over that brooder, just going back to the warm area when they needed to warm up.
I don't have any idea what temperatures you chickens in the coop are experiencing, if you have a heated barn it's likely fairly cold. I don't know if you can provide a cooler area for yours to get acclimated. If you can that would be my suggestion, cool them off and see how they react. Let them tell you if they are ready or not.
Good luck!