1. A desert; a tract of land or region uncultivated and uninhabited by human beings, whether a forest or a wide barren plain. In the United States, it is applied only to a forest. In Scripture, it is applied frequently to the deserts of Arabia. The Israelites wandered in the wilderness forty years.

So, in the time period where Joseph was providing the BoM translation, the definition of wilderness most commonly applied within his culture was that of a forest. More generally, it was ANY tract of land or region uncultivated and uninhabited by human beings, regardless of the landscape.

If I had to choose, I would go with the Mesoamerican model, but fully confess that it really doesn’t matter.