If the main character in a story struggles against the cold Arctic weather, is the conflict internal or external?

In a sense, this is a false dichotomy with respect to Jack London's story "To Build a Fire." While an external conflict is a struggle against something outside oneself and an internal conflict is a struggle against one's own emotions, desires, beliefs, or habits, often the two work together. 

In the case of "To Build a Fire," in one sense, the narrator is engaged in an extended struggle for survival against the Arctic cold. This...

In a sense, this is a false dichotomy with respect to Jack London's story "To Build a Fire." While an external conflict is a struggle against something outside oneself and an internal conflict is a struggle against one's own emotions, desires, beliefs, or habits, often the two work together. 

In the case of "To Build a Fire," in one sense, the narrator is engaged in an extended struggle for survival against the Arctic cold. This would be an external conflict.

On the other hand, the narrative focuses to a great degree on how the cold saps the man's willpower and thus that much of his struggle is an internal one to summon up the reserves of will and character necessary for survival and how he ultimately fails.

Many of these sorts of survival stories set in the wilderness emphasize how a harsh external environment leads to people developing–or failing to develop–inner strength.