The presence of a storm in Shakespeare's plays tends to reflect rage or foreshadow a catastrophe. The threatening, destructive weather on that "fearful night" reflects the dark and dangerous mood of the play. The object of the conspiration to take place is the assassination of Julius Caesar in the hands of Brutus.
There are obviously going to be some problems in the future with the sports, but remember that the simplest, easiest, and fastest thing we can do about those problems is re-schedule. If you have any further questions, just ask me.