There's actually a good article on this by Chris Wickham on this from his book "Land and Power." My takeaway from the article is that the woods weren't necessarily "populated," but that they were actively utilized as a resource area. He also wanted to caution against certain readings of the Latin, in that what were written as wild untamed lands (i.e. "deserta") were part of Christian tropes about the need to convert those areas. In addition, its very important to separate "forest" which has its origin in the notion of a royal reserve of a variety of land types from "woodland," which denotes trees, but were considered common areas for everyone to use.

Although with that said, there's probably a big difference between the Carolingian era, before the land clearances of the high middle ages, but I think the article itself pointed out that it was quite a contested question as to exactly "how forested" Europe was before that era. Given the intensive interaction zone between "Roman" and "barbarian" lands (i.e. the "german" side might have been just as intensely cultivated agriculturally), one wonders if what was true in the high middle ages about a diminution in great forests might have been as true in the Roman era, up until the 5th century at least.