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.