The race has been dominated by an international migrant crisis and attracted $15 million in outside spending. But the special House election to replace George Santos in New York on Tuesday may come down to the most local of problems: an ill-timed Election Day snowstorm.

Forecasters were calling for a half foot or more of snow to blanket parts of the Queens and Long Island district, with much of it falling during prime voting hours. Local leaders warned drivers to stay off the roads.

The wintry mess left both parties racing to rewrite last-minute campaign plans and sophisticated models to understand how the storm might affect turnout. Yet with the result expected to be exceedingly close, the most useful tools were suddenly old-fashioned shovels and snow plows — which wary Democrats feared would be used by Nassau County Republicans to their voters’ advantage.

“For partisans on both sides who believe in divine intervention, the weather will decide whether God is a Democrat or Republican,” Steve Israel, a former Democratic congressman from the district, quipped before the flakes started falling.

“And whether he votes in special elections,” he added.

Democrats have pinned tremendous hope on the district, an affluent and mostly suburban area that voted for President Biden by eight points in 2020 before flipping to Mr. Santos and the Republicans two years later.

The party has outspent Republicans more than two to one and nominated a three-decade political veteran, Tom Suozzi. A former congressman who held the seat himself, Mr. Suozzi promised to return normalcy to the district after the expulsion of Mr. Santos, a serial liar facing 23 federal criminal counts.