Having no water on the embark is a PITA, but not a death sentence. Dwarves get booze from plants (and bees) without any need to add water, so their normal drinking is taken care of.
Hospitals is a bit worse: Some treatment is blocked at the washing stage, and immobilized dorfs eventually die of dehydration, but it's possible to deconstruct their traction benches and remove the hospital zone when they start to get thirsty, and at that stage they tend to crawl to the booze stockpile to drink. Once they've drunk you can reconstruct the traction benches and repaint the hospital zone. Each stint in the traction bench heals a bit, and eventually they're able to work. Obviously, no water means a big infection risk, but death is not automatic.
Edit: There are actually two underground biome types, Underground Chasm (which is "muddy caverns") and Underground Water (which is the normal one). They're not temperature dependent, but rather dependent on a "Water" parameter that can be influenced through an advanced world gen parameter.
Badlands can be completely without pools, in which case you're out of luck regarding surface water without special work arounds, but sometimes those pools are dried out most of the time but can fill up during rain fall, in which case they can be "harvested" into a cistern.