What is distinctive about the way Montresor is dressed is that he is not wearing a costume like all the other people celebrating the carnival. His only description of his clothing is in the following:
...putting on a mask of black silk and drawing a roquelaire closely about my person, I suffered him to hurry me to my palazzo.
The word roquelaire, or roquelaure, is defined by Wikipedia as follows:
Roquelaure (Ròcalaura in Gascon) is a commune in the Gers department in southwestern France. A type of knee-length cloak, which was worn by men in the 18th and 19th Centuries of the Common Era, is named for the commune.
The cloak may have been black, since that was the most common color for men's cloaks. The French name and the French style of the garment are among the many suggestions that Montresor, whose name is French, is a relative outsider and a newcomer to Venice. He does not identify with the Venetians and does not participate in their carnival. This fact has many implications. Among them is that he might be the only person who is aware of the arrival of a Spanish ship carrying a cargo of Amontillado. He is paying attention to business, while everyone else, including Fortunato, is drunk and carousing. If the Spaniards could find no one to buy the Amontillado, Montresor could have gotten the "bargain" he says tempted him to buy a pipe (126 gallons) of the wine without getting an expert to judge its quality.
The important fact that a roquelaire is a knee-length garment means that Montresor will have no trouble building his wall without removing his cloak. A cloak also enables him to conceal a trowel and a rapier easily. We can imagine Montresor in a black cloak and a black mask accompanying Fortunato through the crowded, noisy streets. Fortunato is wearing the most conspicuous possible costume, a tight-fitting jester's outfit and a cap with bells. Fortunato would attract all the attention and Montresor would be like a shadow. Nobody would recognize or remember him. Getting Fortunato to his catacombs is Montresor's greatest problem. It is helpful that everybody on the streets is drunk. (People who are not drunk would probably want to stay off the streets.)
Poe has Montresor emphasize that he is not Italian in the important third paragraph of the story.
Few Italians have the true virtuoso spirit. For the most part their enthusiasm is adopted to suit the time and opportunity, to practise imposture upon the British and Austrian millionaires. In painting and gemmary, Fortunato, like his countrymen, was a quack, but in the matter of old wines he was sincere.
This suggests that both Fortunato and Montresor trade in luxury items such as painting, gemmary, and fine wines. Fortunato may be an aristocrat, but he is an aristocrat who has to earn a living, like most of the Venetian aristocrats. Montresor does not seem to be an aristocrat. When Fortunato asks about his coat of arms, he seems to be making up an outlandish one featuring an enormous bare human foot made of gold. He is toying with Fortunato, who is too drunk to realize it.
Montresor admits he is a poor man. His cloak may be concealing shabby clothing. His poverty may explain why he keeps up a relationship with the rich Fortunato, even though he has received a "thousand injuries." Montresor is noticeably obsequious toward Fortunato throughout the story. They are sometime partners and sometime competitors. Luchesi is another gentleman "wheeler-dealer."