Sauron's arrival greatly changes the Greenwood (also known as Greenwood the Great). This darkening, combined with the arrival of giant spiders, bats, and orcs, gives the forest a new name: the Mirkwood. Only Thranduil's Halls, on the edge of the forest, are saved from this spreading darkness. Bilbo, who is fond of the darkness of Hobbit holes, recognises that the darkness of the Mirkwood is more oppressive and hopeless than a simple lack of light should provide.
The group could, and did, light fires in the Mirkwood - but they soon gave up. The fires attracted "hundreds of eyes". Worse, the light attracted moths, which in turn attracted bats. It was easier, and less unsettling, to avoid the attention that fires provided:
Although it was not yet very cold, they tried lighting watch-fires at night, but they soon gave that up. It seemed to bring hundreds and hundreds of eyes all round them, though the creatures, whatever they were, were careful never to let their bodies show in the little flicker of the flames. Worse still it brought thousands of dark-grey and black moths, some nearly as big as your hand, flapping and whirring round their ears. They could not stand that, nor the huge bats, black as a top-hat, either; so they gave up fires and sat at night and dozed in the enormous uncanny darkness. (Hobbit Ch. 8)
There are references to the Mirkwood in Chapters 7 and 8 of the Hobbit, as well as other works by Tolkien. Indeed the first four paragraphs of Chapter 8 "Flies and Spiders" are dedicated to describing the environment of the Mirkwood.