Yes, the weather plays a factor in presidential elections. Bad weather leads to lower voter turnout, which affects the outcome.
But it affects the outcome how?
Conventional wisdom and even one scientific study say that bad weather favors Republicans. This is because:
Democrats are more likely to live in cities and tend to be less affluent than Republicans, they are more likely to walk to polling places or depend on public transportation. So logically, rain might well discourage more Democrats than Republicans from showing up to vote, or from getting drenched while waiting to vote outside crowded urban polling places.
That may be true, but it's too generic to be helpful, particularly in close races.
Nor is it helpful in this particular election, where early voting is setting records throughout the country.
For example, if Obama is far ahead in North Carolina early voting, bad weather on election day would probably be a GOOD thing for Obama, since it will help cement that lead. (For what it's worth, it looks like Election Day will be sunny throughout all of North Carolina.)
So pray for the rain or sun gods as needed.