My thoughts on said cards.
Amulet: I think this card is more powerful than many people realize. Being able to split trashing between two turns seems strong, and once its value as a trasher has ran out, you can use it for virtual coin or gain silver. Most trashers lose power once your deck is trashed. Sure, Steward can draw and gain coin, but compared to other trashers, Amulet seems up there.
Swamp Hag: Seems like an overall weaker curser, but that isn't a bad thing. Most cursers in the past are almost must buys, so to have one that you won't want to buy in every game is not a bad thing. Although, I still see this getting bought often, but with this being a duration, it seems an attack that you would need to buy more of than normal.
Hireling: An extra card is reasonably strong. In many Prince games I have played, usually the player who connects his Prince to a draw card first ends up winning. Hireling is sort of like that, but you don't need to go through as many hoops and ladders.
Haunted Woods: I don't have much of an opinion on this yet. In some games, I can actually see it helping the opponent, letting them put down unplayed actions for the next turn. Though, later in the game, it can really get in the way of things. It's probably reasonably strong. Also, drawing +3 cards at the start of a turn is like drawing 4 cards since this is already in play and you start with a 5 card hand, so there is that.