Have you seen her bullied away from the feeder? Chickens avoid hypothermia in very cold weather, not by putting on a warmer coat as we do, but by eating more calories. If instead, they are actually consuming less due to being prevented adequate access to food, they quickly get into a hypothermic condition. Extreme lethargy is a symptom and it will progress to imbalance and trouble walking.
To find out if your hen is hypothermic and not suffering from some other issue, give her warm sugar water with a pinch of salt and baking soda while keeping her warmed. You can jump start the rewarming by using a hair dryer on warm setting on her breast and wing pits. If she revives, then you will know she just needs access to more calories.
If she doesn't improve but gets worse, then it's an organic or pathological issue, and perhaps an oral antibiotic is needed.