I believe I understand what your after here: you are hoping to learn about an actual group of people living in the forest that inspired Tolkien in his depiction of the elves. I believe you are barking up the wrong tree, if you'll pardon the expression. I've never seen any evidence that this is what inspired Tolkien.

Tolkien's elves are a direct importation from folklore to literature. He was particularly drawing on the Welsh tradition; reaching beyond the linguistic information in the linked article, he was apparently also interested in the regal nature of the Welsh "Fair Folk", the Tylwyth Teg, which are at the extreme end of Britain and Ireland in depicting a complex elfin society with royal families and hierarchies reflecting the full range of human society.

British elves - and the Welsh variety in particular (probably owing to the dense Welsh forests) - thrive in the woods. A dark environment choked with vegetation that prevents clear views are a good place to imagine supernatural beings. And the forest itself is conducive to allowing the imagination to wander and for the magic of the world to seem apparent. The classic work on the subject is Alexander Porteous, The Forest in Folklore and Mythology (originally 1928).

What are your criteria for being in a forest? Do tropical rain forests count, or are you only interested in temperate deciduous forests?

As a follow up, in Dan Carlin's Thor's Angels, he claimed that some of the Germanic tribes grew up in forests so thick they almost never saw the sun. Do we have any inkling how they would have lived?

There are people who still live in the forest. There are several uncontacted tribes in the Amazon and the forests of New Guinea or the Andaman islands. Aerial photography has shown that they have villages in small clearings and what appeared to be some form of agriculture near the buildings there. From other tribes, it seems as most are hunter-gatherers.

Another type of 'living in the woods' occurred in the European Middle Ages: diseased members of society (such as lepers), or unwanted urban inhabitants (such as, sadly, Jewish town dwellers), were often cast into the forest as a form of exile or quarantine.

As noted in Trees: Woodlands and Western Civilization by Richard Hayman (an 'ok' book – a bit too literary, but I digress), woods were often viewed in the biblical sense as a desert, or wasteland, where people would live or travel for spiritual gain. He mentions Saint Brioc, a Celt, establishing his monastery in an isolated forest, as well as St. Romuald and his long stays in the woods for spiritual growth.

Such stories undoubtedly influenced (and were influenced by) folklore and mythology about the spirituality and/or enchanted nature of forests, and went on to play a major role in the medieval romance works of the 19th century as well as modern fantasy such as that written by Tolkein.

No forest dwellers outside the tropics come to mind, but there are several other groups of people who live in similarly difficult, isolated terrain, especially mountains, swamps, deserts, and harsh steppes (think of the Hmong, Marsh Arabs, Bedouin and Cossacks, as examples of each respectively, but there are many more--Kurds, Seminoles, San/Sho, Mongols, etc.). James C. Scott argues in his amazing book The Art of Not Being Governed that at least some of these people came to define themselves consciously as outside of the realm of states/agricultural civilization, and instead of being "primitive", they were purposely avoiding the costs of civilization. Indeed some of the people who became these non-state people were actually former serfs/peasants escaped from state societies, Scott argues. He argues that with settled grain agriculture, it becomes easy for states and warlords to demand their cut. Grain crops (and most vegetables) are harvested roughly at the same, predictable time. This makes them very easy to tax, because the tax man (or alternatively a bandit) can come around once a year and extract tax/tribute. Non-state societies that avoid taxes, Scott argues, tend to have vegetables like tubers and semi-wild crops that they can simply abandon--for years at a time--and come back to once the threat of extraction is gone. States tend to want to expand (or be conquered by other states), hence they would likely cut down most of the forest as obstacle to growth. Hence, if we expected a full society to grow up in the temperate woodlands, these would likely be ones that have agriculture economies based on perennials, hunting, gathering, herding and above all avoiding states (see below). Much of the text of The Art of Not Being Governed focused on Upland Southeast Asia, an area sometimes called "Zomia". Check out the Wikipedia article, which gives the briefest of introductions to the region and Scott's theories. Here's a slightly longer article on it from the Boston Globe, and if you're still hungry for more, check out this hour long lecture which summarizes all the main arguments of his book (you can treat it like a podcast, there are minimal visuals). Obviously, the book is also one of the most amazing things I've read and I heartily recommend it. Scott concentrates on Upland Southeast Asia, but this argument could easily be extended to a variety of other places. In Europe, states were able to project there power almost everywhere relatively early.

One further issue (also discussed by Scott) is merely calories per acre. Jared Diamond talks about this in The Worst Mistake in the History of the Human Race, how agriculture produces more calories per acre, which leads to higher population density. However, the calories tend to be just from grains (wheat, rice, oats, etc.) and later tubers (yams, potatoes, cassava, etc.) which are high in calories but cannot match the nutrition of a varied diet. This means that the settled agriculturalists, despite their health disadvantage, have a military advantage (more people; higher social organization; higher division of labor) and ultimately relegate non-settled agriculturalists to relatively marginal land (hills, swamps, deserts, harsh steppes, tropical rain forest). Why isn't dense, temperate forest on this list? I can only speculate, but once temperate forest is cleared, it stays cleared for a long time relative to dense jungle, which begins encroaching on cleared land almost immediately. Further, wild tropical forests tend to have more calories available for hunting and gathering (both in terms of flora and fauna). Temperate forests in post-state Europe and North America tended to be included into states. If there was enough need to conduct agriculture in them, there was enough reason to clear them. Unlike the permanent refuge of Zomia, they tended to be at best temporary refuges for bandits, monks, etc (check out this story of a family who escaped into the wilds to completely avoid the state as recently as the 20th century in Russia). Similarly, Scott argues, roads, helicopters, firearms, and trucks have made it so the traditional non-state refuges of a place like Southeast Asia have essentially disappeared since around 1950, since states can more easily project power on all the territory within their borders. There can be temporary escape for small numbers of people, but whole societies like the Elves would too large to escape the state's notice, and therefore extractive power.

Early American pioneers in New England and the mid-west lived in the forest (until they cleared it for agriculture and grazing land).

Few historical human forest dwellers, however, lived in extensive underground complexes or cities within the forest, such as the halls of King Thingol, Nargothrond, or the Halls of the Elvenking (Thranduil) in Greenwood the Great.