Sorry you lost your Wellie.
The black is almost certainly just dried blood. I don't think that is much blood on the shavings.... there were splodges of it all over my coop and running down the side if the roost bar and dripping onto the floor below.
I'm not sure if the cold will inhibit infection or increase the risk. In very cold weather I would expect the blood flow to be reduced and this could perhaps increase the risk of necrosis but probably too cold for bacteria to thrive, particularly in remote digit like a toe. I might be inclined to clean it up with diluted Hibiscrub (Chlorohexidine) or Betadine since you already have her caught and contained, blot it dry and coat it in a thick greasy wound salve like bag balm or pink salve but not try to bandage it. Just leave it to heal and put her back with the others but keep a close eye on it over the coming days.