I'm not gonna lie, this was the first idea I had. The reason why I scrapped it was because I didn't know how I could make it fun. And your execution proves that. You collect wood, get back, fuel your fireplace, and then repeat. It's just a never-ending loop, which really isn't that fun on its own.
Maybe adding more features like hunger and thirst—both requiring you to do a new series of action in order to survive—would be a nice touch to improving the game, but right now, the game doesn't really feel like a game.