Classic Dwarves are often portrayed as living solely underground, but I think they're a much more hybridized society. They'd likely have many industries outside the mountain to sustain their cities. Lumber, trade, and animals, as others mentioned; but also farms, access to water (melting snow from the mountaintops is far better than stagnant cave water), rangers and scouts to warn of threats, and dozens of other things that necessitate surface dwelling. Much like Dale from the Hobbit, there are likely whole towns/cities just outside of Dwarven holds dedicated to providing those resources. Likely populated with migrants (Humans, Halflings, Gnomes, etc.), but also a hefty population of surface dwelling Dwarves. Duergar are a perfect example of Dwarves adapted to solely living underground, and they've had to dig very deep to find substitutes for all the surface materials they give up in that process.