List quotes based on the dog's point of view.

I would like to start by making it clear that this story is told from the third person omniscient point of view. At no point is the story told from the dog's perspective in the same way that London's book The Call of the Wild is written from Buck's point of view. With that said, because the narrator is a faceless, omniscient narrator, readers do get to know what the dog is thinking and feeling. The dog is not an unthinking and unfeeling character in the story. The dog is a developed character with thoughts and emotions, and this is why students typically feel that the dog is the smarter of the two characters. As the question suggests, there are key points in the story in which the narrator tells us what the dog is thinking. The story is not told from the dog's perspective, but we get to know what the dog's attitude and thoughts are based on a particular situation. For example, readers get the following quote early on in the story.

The animal was worried by the great cold. It knew that this was no time for traveling. Its own feeling was closer to the truth than the man’s judgment.
Its fear made it question eagerly every movement of the man as if expecting him to go into camp or to seek shelter somewhere and build a fire. The dog had learned about fire, and it wanted fire.

These two quotes immediately alert the reader to the extreme danger that the man is in. Up until this point, we only experience what the man is thinking. His general thoughts are akin to "Wow, it is colder than I thought, but I will be okay." When we finally get the dog's thoughts, we realize that the man is being naive about the danger of the cold. The dog's thoughts bring about an immediate sense of foreboding.
Near the end of the story, the man is trying to coax the dog toward him, but the dog will not come near him. The omniscient narrator is able to tell us why. We learn that the dog senses danger in the man's tone.

It had never known the man to speak in such a tone before. Something was wrong, and it sensed danger. It knew not what danger, but somewhere in its brain arose a fear of the man.