You are right in identifying that Poe uses the setting in part to create the mood. The mood in this story is one that is sinister, threatening and disturbing as we move ever further down into the catacombs of Montresor's family home and we move ever closer to the grim revenge that he has planned against Fortunato. It is important to focus on how the description of the setting is used to create and sustain this mood. Consider the following quote:
We continued our route in search of the amontillado. We passed through a range of low arches, descended, passed on, and, descending again, arrived at a deep crypt in which the foulness of the air causes our flambeaux rather to glow than flame.
Note the repetition of the word "descended" - we are walking ever further deeper into the dark catacombs, so much so that we are disorientated and we have no idea of where we are. What is clear is that we have arrived at a crypt, where dead people are buried, and that the air is so foul that even the torches are subdued. Clearly Poe is trying to set the mood for the shocking events that are about to unfold.
I think another key passage that helps create the mood of horror is when Montresor finally shackles Fortunato into the alcove from which he will never leave:
In an instant he had reached the extremity of the niche, and finding his progress arrested by the rock, stood stupidly bewildered. A moment more and I had fettered him to the granite. In its surface were two iron staples, distant from each other about two feet horizontally. From one of these depended a short chain, from the other a padlock. Throwing the links about his waist, it was but the work of a few seconds to secure it. He was too much astounded to resist.
What strikes me about this passage is the way that Montresor is able to describe the chains and their location with cool, calm, precision, even while he is planning a most heinous crime and a terrible death. The tone he takes adds to the mood of horror that dominates this excellent but terrifying work of short fiction where the setting is essential to the overall effect.