Limaed: Don't quit. Clearly, there is considerable finesse in using a fire drill.
You must attempt success with local materials.
Sleet, schmeet. When you get a dump of 36-44" in 36 hrs, let's discuss it!
Inuit cannot afford to waste wood in fire drills. There are no trees and driftwood
in useful pieces must always be used for something else. Bone and animal fiber
they have in abundance.
At much lower latitudes like my place at just 53N, of course we have forests in the mountians.
Ignorancy claim that they do have "trees" some of 300+ years in age, but, the root stocks are measured
while the tops are never more than 8-12" above ground, buried from the advances of grazing herbivores in winter.
Browsed heavily enough by rabbits in winter, the wound response from the shrubs is an effective birth control
for the herbivores.