You're right. The first rule if you're lost is to stay put and find a way to signal for help. Burning tires or green leaves make a helluva lot of smoke and are great for signaling.
A shelter would be easy enough to construct and heat in that situation and since it's No. Minnesota, in January, there should be plenty of snow/ice to melt for drinking water. I would imagine the plane, also, has a distress beacon. If no one comes in several days, then leave a message by the plane and make your way to the cabin in daylight.
That wasn't the question though.