I love this question because a reader can answer it in through a big picture lens or a small, narrower view. Let's start with the ultimate effect. The man dies. I could make the argument that this final effect is caused by the man's falling into the water. This forces him to make a fire under the tree that ultimately extinguishes the fire. Perhaps had he not gotten wet, he would have been able to maintain enough logical thought processing to put the fire in a smarter location.
It was his own fault, or instead, his mistake. He should not have built the fire under the pine tree. He should have built it in an open space. But it had been easier to pull the sticks from the bushes and drop them directly on the fire.
Prior to this sequence of events, the man was doing okay. The weather is bitterly cold, and he realizes that maybe the old man might have been right, but the man successfully lights his first fire and warms himself. He's in a solid enough situation where he even smokes his pipe, and the dog is content to stay put and wait for improved weather.
The dog took comfort in the fire, lying at full length close enough for warmth and far enough away to escape being burned. When the man had finished eating, he filled his pipe with tobacco and had a comfortable time with a smoke. Then he pulled on his mittens, settled his cap firmly about his ears, and started along the creek trail toward the left.
The man then chooses to leave, and this ultimately causes his death. He should have stayed put and waited for the weather to improve. I also think that it could be argued that the initial cause is the man ignoring the advice of the old man. Had he listened to the knowledge of an older and more experienced cold weather expert, the man would have likely lived longer.
If you are looking for a smaller cause and effect example, then I would go with the man pulling branches from the tree. This causes the tree to shake and drop the snow onto the fire. The effect is the extinguished fire.
Each time he pulled a stick he shook the tree slightly. There had been just enough movement to cause the awful thing to happen. High up in the tree one branch dropped its load of snow. This fell on the branches beneath. This process continued, spreading through the whole tree. The snow fell without warning upon the man and the fire, and the fire was dead.