Moulting during the winter?

[Stubbymychicken]

Hi! My name is Amelia I'm new here, not new to chickens, I have a one legged chicken her name is Stubby (I'm not creative with names) she is about one year old, and is a blue laced wyandotte. When she was shipped to the grain store where I worked, they sent her with the box divider crushing her foot, we tried to save it however we were worried that she would get sepsis, as the foot was rotting while still attached to her and we decided to cut it off when we was about three days old, she survived, and lived in my room until she got too big, then we moved her to the porch, and built her a pen to be outside in the grass during the day, she's very loving, even though she's feisty at times. We knew she couldn't live alone so we got her a flighty friend and now they have they're own coop for the two of them. It's winter where I live and it gets very cold, so at night they have a special box I tuck them into to stay warm, however at the beginning of fall I noticed stubby wasn't moulting, and she had a lot of built up skin on her head and the back of her neck, I also never saw her dirt bathing, so I started giving her a bath once a month the best I could, I didn't want to damage her skin or feathers so I used a small amount of unscented kitten shampoo, since I know cats have very sensitive skin, so do birds, and I would comb out the built up flakey skin on the back of her head, I figured the one leg made it hard to groom herself, however now it's the dead of winter and she finally started moulting, I'm worried she has a skin condition or I damaged her skin. (Side note I did put baby oil on her feathers after to help her stay waterproof) And I'm also worried that she won't be warm enough since she's just now moulting. She never handled heat well, and has always preferred it cold, so I wasn't worried about winter until now. She has lost a substantial amount of feathers, and has become quite irritable, she's usually very curious and loving but now is aggressive, jittery. She's on a 22% protein and I mix in sunflower hearts and "Kickin Chicken" which is a feed supplement with niacin, omegas and vitamins. She gets veggie scraps from the kitchen from time to time and yogurt as well for probiotics. Maybe I'm overreacting, I just want to make sure I'm doing everything right as I love my Stubby and want the best for her. If you made it this far thank you for reading, any comments ideas or recommendations are appreciated

 

[Yardmom]

What are your temperatures. Do you birds get any supplemental heat? Do you see new feathers starting to grow?

 

[Stubbymychicken]

What are your temperatures. Do you birds get any supplemental heat? Do you see new feathers starting to grow?

Pretty cold, it's been about 20° during the day and around 14-15° at night, we've never used heat in our coops, since it makes it harder for the birds to acclimatize (so I've been told) I'm not opposed to putting a heat lamp out there, the coop does have electric hookups so I can use a water heater. She does have new feathers coming in though, I don't know if she needs help preening, she hasn't had this issue before which is why I'm a little stressed, thank you for your response

 

[Yardmom]

Your temperatures sound similar to where I live now. I think your girl should be ok. I have not had problems with molting chickens being to cold here. Do keep an eye on her, as special needs chickens sometimes need a bit of extra care all around.
Our temperatures are not that cold in the big scheme of things. People keep chickens without heat where I grew up. Temperatures there are regularly -20 and sometimes -40 degrees F.