The word forest originally refers to land that is reserved for the king to hunt on, extract wood and other resources etc. from rather than a heavily wooded area

The word forest originally refers to land that is reserved for the king to hunt on, extract wood and other resources etc. from rather than a heavily wooded area. Even when it was first made a forest (and originally it was much larger) Nottingham forest wouldn't have been entirely, or even mostly closed canopy woodland. A lot of it would have been wooded pasture and heathland. Most of the wooded bits would have been managed by coppicing, polarding and selective felling, and then the forestry commission wiped out much of the rest in the post war period. There's a few bits of ancient woodland in there, but mostly in areas that would have been difficult to get to historically. For a laugh, google forest of Bowland, one of our larger forests that has and has never had more than a scattering if trees.