The Cabin doesn't get you any value immediately when you use it, it just improves your draws later. In that regard, is similar to the Training cards that each aspect got to shuffle in their events, but the Cabin is for shuffling in Wolverine's hero cards, and it doesn't go away after two uses.
What should you be shuffling in? Jubilee is great. Skeleton and I Got Better when you're ready to pay for them/if you lose them. Any of his attacks if your deck is light on those (though Lunging Strike is usually the best, and the other two are more situational). Track by Scent is pretty efficient, can help pay back your initial investment in the cabin. And Regenerative Healing can be good if you want to be able to spend more time in hero mode in the future.
Overall, not something I'm going to play every time I draw it, but there will definitely be decks and board states where I just want to be able to draw more Lunging Strike and this will help with that.