Cull the Weak passive & Hungering Arrow

Can’t find anything definitive and am dying to know. What will benefit from the Cull the Weak passive and get 20% dmg bonus?

Does Hungering arrow/devouring arrow cold rune chill enemies? What if the weapon you’re using has Cold damage?

Here’s a thread that talks about this:

and an interesting comment on the subject:

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Well…if you use a good old Buriza the secondary triggers Cull