What are the ways the author of "To Build a Fire" demonstrated the cold weather?

The author, Jack London, alerts the reader to the cold through a mixture of directly telling readers that it is cold and indirectly describing things that the cold is doing.  
The opening line of the story directly tells readers that it is cold.  

Day had dawned cold and gray when the man turned aside from the main Yukon trail.

What the above line doesn't tell readers is how cold it is, but the line does give a hint.  We are told that the man is in the Yukon.  Readers that know where this region is will know that it is in the far northern latitudes of Earth; therefore, it is a very cold part of the world.  This part of the world does "warm up" a bit during the summer months, but the end of the first paragraph tells readers that the man isn't so lucky to be in the Yukon during the summer.  

It had been days since he had seen the sun.

This tells readers that it is winter.  The man is far enough north where the sun hasn't even been rising over the horizon.  He's in the dead of winter, and that means cold. Eventually, London tells readers it is winter, but he also narrates details about layers and layers of ice and snow for as far as the eye can see.  
By far the best paragraphs about the cold are the two where London has the man contemplating that 50 below zero is 80 below freezing.  Those are big numbers.  If a reader has ever been in sub-freezing temperatures, he/she knows what it feels like.  Then to be told that the man is in weather that is 80 degrees colder than that is a big deal.  But then London delivers some extra details about the cold.  The man spits on the ground, and the spit freezes before it hits the ground.  The man knows that his spit should pop and freeze when it impacts the ground if it is 50 below zero; however, the spit freezes before it hits the ground.  It's way colder than 50 below zero.  

He knew that at 50 below zero water from the mouth made a noise when it hit the snow. But this had done that in the air. Undoubtedly it was colder than 50 below. But exactly how much colder he did not know.