I live in NY too. I am in northern NY near Watertown. I have had silkie broody hatch eggs and raise chicks in my unheated coop in Feb and March with temps sub zero. I would not but a heat lamp in the coop this time of year, hen will more than likely get over heated. I do watch the hatch closely for a couple days before and during to make sure any that scoot out from under the hen I can tuck back under until mama is out of broody hatching trance and into chick rearing mode.
I actually do have a heat lamp from this past winter that's a good idea. I'm going to section her off with some plywood or cardboard so the other hens don't bother her. They like stealing her nest when she's not there. I'll show you where she is right now. My coop is I think 6 feet W, 9-10 feet L and 5 feet H. As you can see I'm not a very handy woman lol