The missing head feathers I would think would be from a rooster mounting her, but if you don't have a rooster, that has to be from head pecking from the other hens and if it's that, poor thing. That looks brutal. Or head scratching? Is she head scratching?
Yea, I think it's neurological. Could be from injury, could be from nutritional deficiency, could be viral, like Newcastle. Looks too cold there to be any fungal issue at this time of year.
I would watch for abuse from other hens, put out extra feeder and waterer and then give her some Vit E capsules for a few days. Vit E deficiency can cause some neuro symptoms, so I would try that. Just pull open her beak and pop a pill in back of her throat. I'd try one a day for three days. A little bit of selenium also, but that should be in small amounts so maybe a food source that is rich in selenium for a treat. If it was me, I'd try that and just wait and see if she comes out of it. You might consider looking for some vitamin mix to add to their water. Not one with sodium for first ingredient, that's mostly for hot weather and not everyday use.