My brooder is in the coop. I put chicks in there straight out of the incubator. Last February it was below freezing when they went in. As long as you can provide an area that is warm enough they will do well.
I’ve had chicks go through a night with lows in the mid 20’s Fahrenheit when they were less than 6 weeks old with no supplemental heat. The unheated coop they were in was well ventilated up high but had really good draft protection. And they were acclimated. My brooder is big enough that the far end cools off a lot more than the warm end. They play in the cold end a lot and just go back to the heat when they need to warm up. That way they get acclimated and feather out even faster and better.
I don’t know what your coop looks like or if you have adult chickens out there already, but you can move that brooder out there since you obviously have electricity out there.
If you can safely heat an area you might be able to just use the coop as your brooder and just heat one spot in that, but the food and water needs to be in a warm spot. That warm spot for food and water does not need to be hot, just somewhat warm. At three weeks age they should adjust to that really quickly and enjoy all the space.