If you are going from controlled temps to a coop with no light bulb and lower nighttime temps, I think they will really suffer.
I feel that the nighttime temps will be too low for your babies unless you run a light bulb for them to huddle under at night (which is what I did for my chicks until they were 5 1/2 weeks old- they are now almost 7 weeks old). They were trying to "get away" from their 60 watt bulbs at 5 1/2 weeks.)
I had them at "brooder temps" until 3 weeks, then out to free range during the day, with a free choice heat lamp available at all times. They went in and out of their coops as they desired.
Our nighttime temps have been down as low as the 50's where I am. After awhile they get used to the cooler temps. It also depends on how many chicks you have huddling.
If they are piling up, they are cold. My almost 7 week olds still huddle up at night, but are gaining weight, and are free from drafts. I won't run any more light bulbs for them anymore once they are fully feathered, since I want them to get their winter down. Our colder weather is coming soon.
Baby them that extra couple of weeks, with a free choice light bulb, if you can do it safely without fire risk.
My opinion is that with winter coming, you want that weight gain on them so they can better handle the coming real cold weather. They probably won't gain as much weight if they are struggling to stay warm.
My summary: if your chicks are coming from continuous brooder temps. that are stable, putting them outside in those temps without a free choice light bulb to huddle under would be too cold. In other words, some adjustment is necessary to those outdoor nighttime temps. Keeping them in the garage for a couple of weeks would be a good second option if you don't want a light bulb in your coop (understandable from risk of fire).