This is what a prolapsed vent looks like when the cloaca is sticking out:
https://www.backyardchickens.com/content/type/61/id/7626978/width/200/height/400
If you have a plastic dishpan, you can give a warm soak to just her bottom, and use a little dish soap to wash her clean. Dry well with a towel and blow dry feathers before letting ber back out. Make sure that she is really dry.
Can you tell us if her bottom has a prolapsed vent or just looks dark and messy? The skin appears darkened. Is her lower belly enlarged compared to the others? I would try to get her cleaned up, but she would need to be brought inside where it was warm for that.is she laying eggs now, or has she...