I agree with the previous post that the whole feel of the story would have been less spooky with the setting changed to daytime. However, Montressor was thorough in his planning, and he could have pulled off the murder during the daytime if possible. Montressor had previously told his servants that he would be away for the evening, knowing that they would "abscond" shortly after his departure. This ruse, which left his palazzo free of spying eyes, would have worked just as well during the daytime hours. The carnival was probably one that went on both day and night, so the revelry would have been underway long before dusk. It is quite possible that Fortunato was drunk long before he met Montressor, and a few more bottles plied by Montressor would have put Fortunato in the desired state of inebriation. Had there been a reason for Montressor to use the daytime hours to seek his revenge, I'm sure he would have succeeded.
The main thing I think would happen here is that the whole story would feel less foreboding and spooky. I think that if the two of them had met in the middle of the day, it would have not felt like something bad was about to happen -- at least not so much. Even though bad stuff can happen in broad daylight, we tend to be afraid of the dark just because it seems spooky. That is, I think, what the difference would be.
I suppose that you could argue that if it had been the middle of the day, maybe Fortunato would not have been so drunk. Maybe if he had been sober, Montresor would not have been able to trick him so easily. To me, this is the main possible reason for a totally different ending to the story. However, it was carnival time and Fortunato could have been drunk at any time of the day seeing as how he seemed to like to drink a bunch.