Ok, I poked it just a little bit and I got a couple of numbers. I’ll try and put them under a spoiler tag just in case anyone doesn’t want to know.
Spoiler
I went ahead and temporarily enabled the show_open_space line in my user settings and measured around one of my hearthlings while they were out in an empty field. I doubt that it makes any difference, but I was using Rayya’s Children in the Desert for this. On Peaceful. The outermost edge of the displayed polygon was a 15x15 block area for their “comfort zone” whose lowest point (at the four corners of the 15x15 square) was 3 blocks in height. At the center, directly above the hearthling, it topped out at 6 blocks.
I appeared to be receiving no unhappiness from my hearthlings in their meager cave dwellings having dug them out to 12x12x6. They were not, however, very pleased with the 4 wide and 6 high tunnels that connected them. I suspect that either a window lined hall (somehow…in a mountain…) or a minimum of 8 blocks wide would help alleviate that. 10 or 12 blocks wide would probably be best in my opinion. And again, likely a minimum of 6 blocks high to prevent them from feeling like they’re scraping their poor little heads on the ceiling.