I got the Headless Horseman's Hearthstone last night. It shares a cooldown with your regular Hearthstone, so no advantage there.
What's annoying is that it doesn't recognize the Mission Research benefit of a 40% cooldown. When I used it, I got a 15-minute cooldown (reduced from 30 min due to the Guild perk), not the 9-minute cooldown. The regular hearthstone also gets the 15-minute cooldown when you use the HHH.
Unless you want the flaming-pumpkin effect as you hearth, you need the one extra slot of bag space, or you get stuck a lot, it doesn't seem worth the grind.
Edit: I just confirmed that the cooldown of my regular hearthstone, when used in Boralus, has been reset to 15 minutes. Crud.
Edit #2: Evidently this has been fixed. The cooldown on both hearthstone tooltips now reads 9 minutes.