I am not sure if "horning" is a word at all, and if it is; it's not being used properly. Horning, does have meaning though. It is a place in the world where they have discovered many new things for archeology. So, that would make it a name, which would require a capital. We all know that you aren't meaning that place, so "horn" would be more proper.
Think of it this way:
You wouldn't say: The appling on my counter is green.
You'd say: The apple on my counter is green Good luck.