When I was in Girl Scouts, we used to do pothole cooking. Dig hole,
build wood fire, wait till it had good hot coals. Then we put in
packages of food wrapped in foil, covered that with wet leaves and then
dirt. Kept it buried a coupld of hours and then feasted.

You could do something similar with charcoal, it seems. Get some good
hot coals going, cover with wet leaves or straw, wait a couple of hours.
Doesn't seem the ground can be frozen very far down yet, and this
method would keep most of the heat on the hole.