Yes, the weather plays a factor in presidential elections. Bad weather leads to lower voter turnout, which affects the outcome.
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.