Actually, I'm curious to know if the deforestation caused by human settlements is currently related to the amount of lumber demanded for the construction of buildings.
IIRC deforestation in history wasn't caused so by buildings, neither by house heating - those consume too little wood to have much impact. The main causes were charcoal burning for metal industry (should get in the caravan arc), ship building (far from in the game), and simply burning the woods to make more land for farming (which I guess is the current in-game deforestation).
Wood is used in everything in a pre-modern society, such that wood as fuel--whether for cooking or for bricks or for meta--was not the only significant draw, and wood for scaffolding in the construction of stone structures consumed much more wood in the late Greek and early Roman period than earlier construction projects for mostly wood structures. Still, deforestation was not simply caused to get wood, it was also caused to create farmland or simply deny ecosystems services of forests to groups who were better suited to them. Urbanizing powers found that both their own people and competing, less advanced societies, were made weaker by large-scale destruction of forested regions, regardless of whether the wood was put to good use.
On the other side of things, oftentimes primeval forests could not regrow due to environmental changes (whether climate or soil regime) so any damage done to certain forests was, by their very nature, permanent.