Sorry to hear that, it seems that you have misunderstood how the game works quite a bit. To climb walls you can either use grappling or perform walljump by running into the wall and pressing W. You've also misunderstood how the inventory system works, you can collect as much wood as you want and it is all saved in your inventory, the cost of one fireplace is one wood, therefore you indeed can save wood for later.
The coldness is a core part of the game, also there are multiple ways to restore heat: campfires, crystals, re-entering the cabin. I hope this cleared up some thing and that you can enjoy the game fully.