I know exactly the weather you are having as I am in Upstate NY too.I'll go add to my profile, but we are upstate NY. Just starting to get frost at night. It's been chilly a little earlier this year, but we expect a winter with 20's at night and 30's during the day.
I think the advice of focusing on the windows and reopening those vents up high (a good 3-4 feet above the roost bar) is what we're going to work on this week - by Friday when it's supposed to be in the low 20's (which is a little bonkers before Thanksgiving). I've also got to spend the week convincing my 5-year old to put on her coat in the morning :/.
This is how I ventilate my coop:
Soffits open. Gable vents open. Both backed with 1/2" hardware cloth.
Pop door open. Ridge vent open.
All the above venting is left open year round.
Note the crack of light coming in on the top of the right window. They are not tight windows but they do not allow drafts on the birds.
I have two windows, that are not near the roosts, that I leave cracked open.
Try for something similar and your birds should do well.
Keep the bedding dry.
IMHO, poop boards are the best asset for keeping the coop clean and dry.
If you have a waterer inside the coop, make sure it is a closed style.
This is what I have in the coop. I'll be installing the thermostatically controlled bird bath heater in it today.