Just guessing but the tracks leading up to the kill site look like they are the rooster's track. In that type of snow rooster's leave an indistinct and wandering track that looks very similar to those tracks. Based on the neck wounds and the wing marks in the snow, my guess is that an owl was the predator.I put pictures on there of the kill site and the tracks of my critter(s).
You might just want to look to scare yourself knowing people live and flourish in conditions like the pictures show... BTW warmed up to 15 below now!