In "To Build a Fire," why does the man still chew tobacco even after ice forms on his chin?

There are a variety of reasons for this, most of them subtle, and not necessarily crucial to understanding the story or main character, but it's an informative piece of imagery nonetheless.

First, tobacco contains nicotine, which is addictive. During the time period at which the story takes place, tobacco use was widespread and socially acceptable, and so it should come as no surprise that the man might be addicted to it.

Second, the man is...

There are a variety of reasons for this, most of them subtle, and not necessarily crucial to understanding the story or main character, but it's an informative piece of imagery nonetheless.

First, tobacco contains nicotine, which is addictive. During the time period at which the story takes place, tobacco use was widespread and socially acceptable, and so it should come as no surprise that the man might be addicted to it.

Second, the man is in the middle of the wilderness, and keeping up a tidy appearance is the least of his concerns. He has no practical reason to expend effort cleaning his beard or moistening his lips enough to spit out the tobacco juice, nor to deny himself the enjoyment he gets from chewing it just to avoid the messy accumulation of ice.

Third, the nicotine in the tobacco acts simultaneously as a stimulant and a relaxant. This isn't a casual hike for the man, and he needs his full attention focused on traversing the icy ground safely. He also needs to conserve his energy and proceed methodically, so the tobacco, or more specifically the nicotine, may help him achieve a more zen-like state that makes the task easier.

Finally, he may simply chew tobacco to stave off boredom. Chewing gives him something to do that might take his mind off the monotonous physical and mental task of hiking. 

As a side note, London devotes considerable attention to the distasteful appearance that the icy spittle gives the man, and this may have simply been intended as a means for us to imagine how unsavory and haggard his appearance is, and to think of him as existing in a less civilized state.