Strangely, there are times where it would be a really good idea to build a fire under a tree. If you are trying to escape detection and want something to try and dissipate the smoke and prevent people from far away finding your fire, it can be a good idea. It can also act as a shelter from rain if you are lighting a fire in the rain.
The problem is that the main character in the story is lighting a fire under a spruce tree that is absolutely drenched and hanging with snow. When some of it melts, you are creating rain or even bringing down a lot of snow onto your fire, in this case leading to the man's death.
It is a mistake to build the fire under the tree because the heat of the fire will melt the snow on the tree and then the resulting water wil extinguish the fire.