I’m in NY too. With five 11 week old silkies. They have a bantam Cochin who is 15 weeks in with them but otherwise they do great in the snow. Mine had a heater but it was causing humidity issues so I turned it off. They do great. I’ve had them out since before Christmas. So they were outside through the 3 feet of snow we got.
At night they all huddle up on floor of the coop together and keep warm. I had a small roost but they prefer to pile. I think six weeks is when I put mine out. Because my chochin was 10 weeks and they’re four weeks apart. So I think yours will be okay. As long as your coop isn’t drafty and they don’t get wet they should be fine.