First of all, thanks for the feedback :)
The furnace is unlocked once you get the smelting skill. The first smelting skill is unlocked by farming iron and copper ore in the area behind the Big Log on the right.
Note: Iron is present in the south while Copper is in the north of this area.
I agree there is an info missing on how to get this skill. I haven't come up with a good idea to fix it yet.
Anyhow, thanks again for playing our game! ;)