Blizzard Crown question

Does the extra cold damage on the implicit of Blizzard Crown affect Ethereal Knives? If yes, what I've I'm using Hrimsorry to convert all my physical to cold?

Yes, Hrimsorrow is irrelevant that converts the phys.

Short explanation, its like having added cold support attached to your skill

Slightly longer explanation, take the value and multiply it by EK's damage effectiveness (220%) and add that to its base damage

so if your blizzard crown averages at 100 cold damage you'd gain 220 cold to the base damage of EK plus the physical damage it does by itself. As you are wearing Hrimsorrow that physical damage is then converted to cold as well.