I feel like switching between e.g. a bow and an axe to cut trees down every minute is quite tedious at the moment by having to open the inventory and equip it manually. Could we assign a hotkey to an item to fast equip? Or alternatively if we try to do an action that needs a tool just let the character do it without having to equip it first if it's in the inventory? 

That's a good suggestion, I added it to the list and will see how to make it easier. Using the item from backpack would probably be best to not have to do the tedious clicks, but it would have to be disabled on "walk on a tree", so you wouldn't start cutting it down when running from an enemy ;)