Can it become too cold for my hen while she is going through a hard molt in winter?

One of my young barred rock hens (about one year old) is going through a hard molt right now. Her neck lost all feathers and is practically naked. It's December here in Northern California, not that cold of course, but it gets down to 28 degrees F during night time, which means frost on the ground. The chicken coop is built from some thin wood. Though barred rocks are supposedly cold tolerant, i wonder if going through the hard molt puts that hen at risk of being too cold. As i don't have any previous experience with this issue, any comment is highly appreciated.

 

She is losing feathers all around, the neck is just most evident... I also see new feather coming out slowly to replace the lost ones. So, given that she stopped laying and that it's the season (I do not extend the daylight time by installing a lamp), it pretty much looks like molting... And yup, I'm giving the chickens more protein this time around. Like you said, hopefully she is going to be fine... Thanks for your support!