Looks like you've already gotten some great advice, but wanted to say welcome to the site! 

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Thank you, it is a red light so I thought that is less irritating. It did sort of start around then . I think we might be past the real super cold so maybe I’ll pull the light.Welcome to BYC!
Chickens normally don't like light during the night, it can make them very stressed. I recommend getting a heater that doesn't have a light, such as Sweeter heaters. I have the side mount and hanging ones, both work great!
There could also be a small animal scaring them and causing them to not roost there.
As for the one missing tail feathers, she could either be getting pecked at or starting to molt. If you have a rooster that may also be the cause.
I live in Southern Ct. It’s been getting down to single digits at night. Coop is 25 sq feet for 6 chickens. Ventilation is very good maybe too good which is why I need a heater. Smells fine, I use crushed up autumn leaves as bedding and I’m using the dry method. I haven’t seen evidence of parasites or mites yet but I may just clear the bedding and inspect and start fresh again. I think both run and coop are pretty critter proof as I use .5 inch galvanized mesh and I custom built the coop and run. But you never know. I have a door that has a gap I’m not super happy with.Where do you live? How cold is it? Do the chickens really need so much extra warmth?
Did you check on parasites?
Is there a chickenwho is bullying the others?
How big is the coop? And how much room is there left/right and above the chickens if they roost And do you have much ventilation?
Does the coop smell badly or okay in the morning?
Can they go out after sunrise? Or do you open the coop after a certain time?
In other words, we need much more info to find the cause. Photos are very helpful too.
and Welcome to Backyard Chickens.
to have you here with us. Enjoy your time here at BYC!
Glad you joined.