Having done some fairly rigorous testing with extreme cold in DF, I can confirm that creatures will die of frostbite, but it takes quite a while. They also have to be in contact with the cold object for a long time, and it has to be really cold.
EDIT: Sorry, had to leave the computer I was working on. Anyway, yes, frostbite is possible, but rarely fatal in the short term. It took me quite a bit of tinkering to get a material which could reliably cause frostbite, and it ended up being around 2500 U. As a liquid spray, it would coat the target and cause frostbite on all their skin in a relatively short period. Unfortunately, this did not seem to be reliably able to kill on its own, though I'm pretty sure frostbite will cause death by infection if left long enough.
As a weapon, it was nigh useless, as it would only cause the wielder's hand to freeze. When I made a bolt out of it, it only caused frostbite when it lodged in the target, and it still took a while before there was any noticeable effect. Unless it managed to freeze a vital organ (the impact of the arrow/bolt would probably kill/seriously wound the target anyway in this case, as frostbite is very localized), I doubt a frostbite-based arrow/bolt would kill in any reasonable timeframe.