The neck marking is part of a tattoo that was magically placed to mark Kyon as Lucaon's servant. I think it has to be magically removed--it's in his skin. It was added when Lucaon met Kyon and put his hand with his own tattoo to the back of Kyon's neck, and it's where Lucaon likes to connect magical chain to Kyon.
With the snow and the introspection, I was worried that maybe Kyon had killed Lucaon when Lucaon went zero, and now he was going to kill himself. I've seen K dramas like that. But I hope not. I am hoping maybe Kyon slices his throat or his hand a little to force a wounded Lucaon to drink from Kyon because that's happier (Lucaon will heal Kyon). It may be neither. Knives, snow, moodiness--could just be a Monday.
I wonder what he'll be doing with the knife later on?(〜 ̄△ ̄)〜