Is it possible, if placed on the skin for a prolonged period of time, to get frostbite from snow?

Yes. Frostbite can occur w/ exposure to very cold temperatures( esp.W/ wind) and snow in as little as 3-5 minutes... Your question is somewhat confusing , however, w/ your reference to isolated snow exposure. See your physician immediately or go to er if you think you are suffering from frostbite ...