What a nice mood, Orks aren't always slaining Humans with their axe, sometimes they use it to chop down trees ;). I have a couple advice for you concerning the game. Especially as our game also uses the fire as mechanic and because we struggled to keep our game "balanced".
First, you didn't use any static UI elements like a fire health bar, maybe you didn't want to, but when you're far from your fire, I think you need a bit more info about how it's going. You could make the Ork speak like "The warmth of the fire keeps my heart ready for tomorrow's battle" when the fire is at max health. And something like "If I don't bring up a log right now, I will probably never see my children again.". Those are exagerated sentences of course but you could add some more depth with such a way ;).
Also, I think your game is not balanced, you can't keep your fire alive more than 2 minutes if you don't catch a shroom. Otherwise you can't reach the trees, chop them down and bring the logs back in time. I think this problem comes from your level design. In order to regulate that you could place a ring of trees around the camp, as "starter pack" , and spare them as you go further. This would allow your player to store a bit of wood. Having some storage of wood will then allow him to explore a bit, which is interesting in your case because your game is very moody.
I hope that this could help you, don't hesitate to reply to me as we can talk about it ;). Still a great entry, well done!