No idea, but another comment claims it works for severed body parts. I'd assume that freezing an attached bodypart would have complications due to circulation being hindered in non frozen parts of the body, and it would be painful.
Don't think a 21st century ethics board is gonna be onboard for doing such an experiment either.
people in siberia/artic regularly freeze their fingers, no need to have cobayes.
Blocking the circulation in the hand does not make someone die, many people survived loosing an arm for a reason.
What must be said though is that while freezing allow for partial body rescuscitation, let's not be fooled. The mice or body part might behave normally, but the body has suffered from a lot of possibly permanent damage (conformational changes, oxidative stress). I expect rescuscitated humans to have a lower quality of life and reduced lifespan, although that's fucking worth it for being rescuscitated!!
One reason is that ice has that annoying property of taking more volume than water. This has consequences. However modern cryogenics aims to vitrify water, which is a special kind of ice that does not take more space!
What people don't know is that structurally preserving organs AKA cryogenics, is a solved problem. Researchers have done that sucessfully to a pig's brain, preserving 100% of its structure. The current issue is that while we can preserve the body without structural losses, we don't know how to reanimate it because the chemicals they uses become toxic upon reanimation and there is no known way to extract it fast enough.
As a reminder, before rescuscitating humans, cryogenics will allow better preservation of blood and organ donations.