Solid entry, fits theme. I wish the pickup/drop buttons were left click and right click, I think it would feel better.
So I start up the game. WASD to move, okay. So I move around and go to the axe... but I miss the part that says press E to pickup the Axe, so I reload the game to figure out what button to press. Pick up the axe..."press E to drop the axe"... but I just picked it up lol, okay, how do I swing... I can't, I'll go to a tree then click, nope wait, press F. Okay now pick up the wood, oh wait the axe drops, okay. Some inventory management, could be good, adheres to the theme. So I do that a few times, throw wood into the fire... Okay now what? Is that it? Oh the fire is growing and I need to find a house, but where is the house? I don't really want to tediously feed this fire while managing the inventory, I'll just run off into the darkness...Oh, monsters, Well I'll just keep looking... *Look* *look* *look* *dead*... okay... interesting game. (I just wanted to share this little story of my thinking, not to be an ass, but because I think it's important for design critique).
As a jam game I understand why it falls a little bit short. Your game's inventory system reminds me of adventure, where you have to leave items around and come to pick them up. You could have made a quick little trade/puzzle sequence where you need the axe to chop wood, then start fire, then burn a fence, where you'll find a rusty key, which unlocks the door to another mcguffin which unlocks the way to the other mcguffin, until you reach a point where you need to manage all these items to destroy Evil once and for all. Or keep it even more simple, and just keep the fire from dying. Looking for the house was not fun for me.
There is potential here though. Good job getting it done and submitted to the jam!