No, she won't be too cold. My old hens, nearly 5 y.o., are molting right now. Two are almost finished up and two still look like walking pin cushions. Mother Nature gives them what they need - in this case, feathers - when they need it. The extra protein feed will help, so would some high...
Sounds like she is doing a mini-molt; fairly common in first year hens in the 8 to 9 month old range. And yes, it does make them sensitive to touch.
I would double check for mites, just to be sure, but I'll bet she's molting.