I feel we need to establish firmly whether we're talking about embarks that are technically impossible to create a successful fort on (c.f. an all-gem map, slade pillar, etc.) and ones that are just extremely difficult, but not literally undoable.
The former case is probably only possible with direct intervention in the game somehow, whether through dfhack or raw modification. Without enough social ties to cause tantrum spirals, a group of seven dwarves is actually pretty resilient; even in the worst circumstances, as demonstrated in this thread, it's not unlikely at least one dwarf will survive long enough to burrow underground, at which point they can probably access enough resources to stay alive.
In the latter case- I've had fairly benign embarks turn sour (and once, I think, result in an instant crumbling) due to embarking on a frozen river just before the spring thaw. That's literally just chance, though, so I won't count it. A freezing/glacier biome with no cavern/magma/clown layers would certainly be up there- at the very least, severely restricted drinking sources would limit your stable population to maybe 80 dwarves tops. As pointed out in the OP, without water most injuries (and definitely most infections) become a death sentence. You can achieve this without modifying the raws (but you do need to mess around with gen params), so I say it counts. If you make it an Evil glacier, that also curtails any hunting for meat you might do, so basically all food and drink would have to be imported. If you could pump out enough trade goods to keep everyone fed and watered, you could probably carry on for awhile, but without flux stone, fuel, or magma, sieges would eventually force you to choose between defence and provisions...
Alternatively, if you're not above modifying the raws, playing as a race without mining or woodcutting labors enabled would make hard real quick.