Thunderfoot said:ACtually all of the above posts are slightly wrong, becuase the real answer is...it depends.
All of those who don't also amount to "that depends" at least. Which a couple do.
In your case though, frostbite was much less of a worry than immersion foot (or in this case hand). It is a condition also known as trenchfoot (can you guess why). The extremity is submerged or even damp and then exposed to extremely cold temps (below 50) for extended periods of time (usually in excess of an hour, but can be considerably less do to other factos).
Two inaccuracies -
1)Cold and damp is often not sufficient. Trenchfoot generally also requires constriction of the extremety - like being in a combat boot. If the extremety is not constricted, it takes a lot longer for the condition to develop.
2)Trenchfoot does not require "extreme" cold - it can happen in conditions up to 60 degrees Farenheight. It was fairly common in Vietnam, which has winter average temperatures in the high 50s.