Just for fun, I decided to crack open the game. I was A: Able to craft the furnace without trouble, and B: Able to place it without issue.
1: Did you let it craft? Crafting takes time in the game.
2: Did you try a flat area and look for the object to have a blue highlight?
Seems that crafting it, taking it from inventory and placing it in the toolbar is not enough. While the Inventory is open it will show possible locations, but in spite of this, you can only place when the inventory is closed and the item is selected in the toolbar, which is not intuitive based on the visual cues.
I worked this out about 5 mins after this post but can't seem to delete. At least it might be useful for someone else later.