Firstly I would like to say that you have done really well to get a production bird to 9 years old. She must have some good genetics. I hope you have raised some chicks from her.
To me her abdomen looks swollen as well as red. Have you compared it to other hens? This is best done at night whilst they are roosting, by cupping your hand between their legs from behind and feeling for any fullness. Unless her posture is more upright, that part of her body should not be coming into contact with the ground and poop sticking to it. My guess would be that it is her own poop snagging on her feathers because she is a little swollen. Poop would be sticking further forward if it was from resting frequently on soiled ground. Don't beat yourself up about clipping the feathers. Once poop gets caked on, it is like concrete and only a good long soak will get it off. A damp cloth will not do it and even then it is not practical to be getting her wet in the middle of winter. Those feathers are better removed so that you can see if there are any sores developing. The skin looks fine at the moment apart from the redness, which may be as much from exposure to the sun as the cold.... you don't specify your location, so I'm not sure if that is likely in your climate..... a person in California has a different idea of cold to someone in Alaska! I would just apply a good slather of Petroleum Jelly to keep the skin protected and supple or any other greasy ointment you have. I have a thick pink salve which is produced for wounds on horses and contains a little citronella to keep flies off and I use that for such things on chickens and it works great on scaly leg mite too, although your girl's legs clearly don't need that..... at 9 years old her legs look amazing!
As regards her problem with walking a couple of months ago, that sounds very much like an outbreak of Marek's disease to me. I have had several birds make limited or even full recovery from such sudden debility. Some took months to regain enough use to free range whilst others miraculously fully recovered after a few days. Most of what you read about Marek's is the worst case scenarios because those are usually the ones that get diagnosed (via necropsy when the bird dies) but there are milder strains where birds can recover from outbreaks but unfortunately will be prone to others in the future usually at times of stress. Your girl is old to be exhibiting the disease (it tends to hit adolescent birds most frequently), but it may be that now she is older her immune system is not so strong and it is surfacing or perhaps she has only recently been exposed to the virus this past summer. Of course it also may not be Marek's, it just sounds identical to how some of my Marek's birds have developed symptoms.
I would probably check and regularly monitor her breast condition.... feeling the breast bone area of the bird gives you an indication of their overall body condition. If the bird starts to lose muscle and the bone becomes prominent and sharp under the skin, that is a good indication that there is an underlying illness or internal problems. Muscle wastage is another symptom of Marek's, but like all Marek's symptoms, it may or may not happen. I would be inclined to give her some extra special treats like a little meat (a few small slivers of raw liver are good or cottage cheese or scrambled egg a couple of times a week and a good quality poultry vitamin supplement like Poultry Cell or Nutri Drench to support her immune system and a good slather of grease on that butt every couple of days.
Good luck with her.
