Not sure if anyone's mentioned it, but it looks as if this has a pretty nasty combination with Possession.
"Oh, you didn't want a hand of all Copper? TOO BAD"
Using it to put Copper on their deck probably isn't that smart. It means you didn't spend as much money as you could have to buy yourself a card. I don't think it makes Possession worse really. You leave them with a bad turn, so they buy nothing and Haunted Woods stops working.. that's what would have happened if you hadn't Possessed them anyway, just 1 turn sooner.
I don't understand what you're saying here. They have a bad turn, then you just do the same thing again on your turn (Haunted Woods -> Possession -> put garbage cards on their deck). Thus your opponent has garbage turns every turn for the rest of the game.
They can only do this if your deck is capable of drawing itself. In a typical deck, you're going to have an average hand for them to possess after your dead one. That average hand won't be likely to be able to get 5 dead cards in it. But I suppose it will still be strong with Possession. Could work out more like the Possession/Forge pin though; which is pretty uncommon.
This is indeed a combo with possession. (unlike possession-forge, which has such bizarre requirements it will never work in practice)
I've been on the receiving end of this combo and can confirm it's very painful. The requirements are:
* both possession and haunted woods on the board
* a village
* a way to trash cards
Then you both spot this combo and go for it. One of you will be slightly faster then the other. You will possess, buy a copper, topdeck 5 bad cards and they have a dud turn. You will possess again, and now you get to play with their deck minus the 5 bad cards. That is probably good enough to draw the deck again and voila 5 bad cards on top again. You do need to buy a copper every time you possess them, so you should also include a way to get rid of that copper on your own turns.
All in all it's about on par with Possession-Ambassador and Possession-Masquerade - if you end up on the losing side you simply lose the game.
But if you both accept this race as 'the new game to play' it's still a fun one to play out. Just resign once you're blocked out in stead of letting the agony get to you.
In theory you could hope to buy so many coppers on the turns you still do get to play that your own deck becomes so bad they can't keep it up, but no... no thanks.
The bold part is where I get lost. Why would an average hand be likely to be good enough to draw the deck? Especially in a deck with at least 5 dead cards? Also, on top of needing to be able to draw your opponent's deck, you have to draw your own deck, so that you can reliably play both Haunted Woods and Possession every turn. And if you can draw both your own deck and your opponent's deck reliably, isn't that basically what's needed for the Forge pin? (Plus they need to have a Forge of course).
One other thing, if you do get this working, you wouldn't just need to buy a Copper every turn... you would have played all or most of your opponent's deck, so you could probably buy another Village or other engine piece.
*Edit* Never mind about the Forge thing, I just remembered that they can't actually play any cards for Forge to work; you have to make them draw their entire deck on your own turn with Governor or such.