This is my brooder built into my coop. I've put chicks straight from the incubator into it when the outside temperatures were below freezing. I use a heat lamp, not a heat plate. When it's that cold the plastic goes all the way to the top of the sides but that "chimney" where the heat lamp is still gives good ventilation. The side with the heat lamp stays toasty but sometimes I find ice in the far end.
A broody hen can raise chicks when the temperature is below freezing. Even very young chicks can spend a surprising amount of time in the cold, just going under Mama when they need to warm up. That's the type of environment I try to provide. An area warm enough that they can go to when they need to warm up but also an area cool enough if they need to escape the heat.
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Your heat plate should provide that warm spot like a broody hen does, provided they can all fit. I've seen posts on here where people use heat plates outside in cold weather.
Your older chicks aren't that far from not needing any supplemental heat. I've had 5-1/2-week-old chicks go through nights with temperatures a little below freezing with no heat provided, colder than what you are facing. Exposing them to those cold temperatures helps acclimatize them and I think helps speed up feathering out.
If it were me I'd move them out. Don't be surprised if they don't use the heat plate as much as you think they should.