Final answer:
The man needs to build a fire to melt the ice covering his face, which is preventing him from eating. This is a crucial survival step in the extreme cold conditions he is experiencing.
Step-by-step explanation:
The passage provided vividly illustrates the peril of a man in extreme cold conditions, underscoring his need to successfully build a fire to avoid frostbite and potential death. From the given options, the correct action the man must take to be able to eat is melting the ice-muzzle that has formed on his face using a fire. This is clear from the excerpt that emphasizes his immediate and careful efforts to build a fire to melt the ice on his face and warm his numb extremities. It should be noted that without doing this, he cannot eat the food he carries, as he would be unable to open his mouth.
None of the other provided options accurately reflect the situation depicted in the text. The emphasis on fire-building suggests the importance this task has for survival in subfreezing conditions. Fires can mean the difference between life and death, serving as a heat source, a means to thaw frozen clothing or body parts, and a way to cook food. It can also be mentally reassuring in dire survival scenarios, as suggested by the comfort the dog finds in it.