Some reviewers analyze the story literally instead of searching for symbolic significance. A literal interpretation suggests that Gogol's story is about the importance of olfactory perception, which is obscured in Western society by a focus on vision and appearance.[4] This interpretation is consistent with Gogol's belief that the nose is the most important part of a person's anatomy.[5] Major Kovalyov obsesses over his appearance, cleanliness, and rank. His behavior reflects the influence of vision-oriented Western culture that emphasizes deodorization and hygiene.[4] And yet, he is deeply upset when he loses his nose, which shows that olfactory sensation is still important despite Western influence.
I think the casket is a symbol of death and it is also a symbol of cruelty of the narrator that he took Doodle to see it and touch it to emphasize that they thought he was going to die so needed to be brought face to face with it.