Can acupuncture help speed up recovery of frostbite on the hands?

No: I am unaware of any literature that reports acupuncture has any benefit for frostbite.

Yes: There is a fair amount in literature regarding use of acupuncture to reduce pain associated with peripheral nerve damage due to frostbite. It can also be used to help prevent nerve damage. It can reduce stasis of blood flow in effected tissue.

Perhaps: Although a classically trained neurologist, who has been taught that acupuncture only helps pain, I have seen amazing results, such as cessation of limb swelling, and resolution of sensory loss after a few sessions of acupuncture. I would suggest that you have nothing to lose, and potential of benefit, so, try it and see if it works. Let us know outcome.