Sanctume, I have to say you're incorrect. Using pumps fully underground but in the lowest glacier layer (directly on top of the conglomerate containing the aquifer) caused the water to turn to ice immediately when output from the pump (it seems the glacier temperature is -5 degrees centigrade). Only when that failed did I try to use a cave-in, only to have that ice melt as the aquifer has a temperature above freezing. When the aquifer then was exposed to the open air it froze where exposed.
Yes, freezing exposure is the easiest, but that requires exposure to the hostile local wildlife, and I'm keen on not exposing my dorfs.
I eventually canned that embark as the biome turned out not to be reanimating. My current embark is reanimating except for the top NE corner, which contains an aquifer in an ocean biome. My first embark attempt ended in disaster, as an undead yeti tore the whole party, complete with animals, to shreds. An evil rain caused both miners to despair (apart from generating nausea and blisters all over the body), so they didn't even try to dig. I then crashed and retried a reembark a lot of times before I managed to dig down before the animals from the previous embark were reanimated, then get a well going before thirsting to death, and then manage to build a butchery in the safe corner and butcher a draft animal to get something to eat (nothing except weapons animals, and a single piece of wood was salvaged before the opening was bricked over). Boy, is it frustrating to see the dorfs hunt vermin rather than finish the butchery and slaughter an animal!
The surface was further cluttered with 3 immigration waves (one even appeared in winter) and a caravan (sans wagons), despite my fortress being completely sealed and having no trade depot. The trade liaison didn't make it either, of course.
The surface was eventually purged by trapping and atom smashing the undead that filed in through one of the entrances I made (the other one just confuses invaders, who generally refuse to enter, or, if the do, exit again). A dark tower siege then failed to find any of my entrances, despite entering on top of the confusing one, but did the great service of slaughtering 4 undead yetis (while I have one caged), reducing the population greatly in favor of living birds. They also managed to fight and kill a titan that then reanimated to be fought again, and the undead killed by both yetis and the titan turned on their former partners, resulting in a rather messy surface. 10 days before the siege year was over they'd finally drifted across the map and 6 if them found the entrance and were caught in the traps. The rest of the force left when the year was over.
With the lengthy description above in mind, I'd say you'd have to be very lucky to be able to dig down and seal yourself in, but once safely underground clearing the surface is mostly a matter of careful and methodical work (That's the reason I save scummed the failed reestablishment attempts, since I think the embark was about as cluttered as was survivable already). I almost succeeded in clearing out a cavern overwhelmed by undead that recruited every critter entering it by atom smashing all that filed in through my entrance and cage capturing the ones too big (cave ogres, one GCS (out of two), and jabberers). I had to rebuild bridges twice because they were destroyed by big critters. With 20 or so critters left they stopped coming, so I made two raids with my poorly equipped militia to clear things out further, but before the next push an FB entered and was recruited, so I'm probably back to square one. I've tried starting a fire raging through the cavern, but that didn't seem to have much of an effect on the undead. Divide and conquer is an option (using cave-ins to partition the cavern into manageable portions).
A parallel thread concerns the biggest threat to the fortress so far (reanimated wool)...