Mr. Trump also benefits from intensely loyal fans, some of whom have driven many miles to help him out, without having any contact with the campaign.

Edward Micheals, a 66-year-old truck driver, said he drove from his home in Dallas, Texas, to volunteer. “We don’t want to take any chances,” he said in an interview at the Machine Shed restaurant in Urbandale on Thursday, where the former president’s eldest son, Donald Trump Jr., rallied supporters.

Amid all of this uncertainty, the biggest wild card is Ms. Haley.

Until late November, she had almost no campaign staff on the ground in Iowa. But then the political network founded by the billionaire industrialist brothers Charles and David Koch endorsed her and handed over their organizational muscle and financial heft. The group, Americans for Prosperity Action, has been knocking doors across Iowa for Ms. Haley, trying to reassemble the coalition of wealthier, college-educated Republicans that brought Senator Marco Rubio of Florida close to victory in a fast finish in the 2016 Iowa caucuses.

The weather may play to her advantage with that group. Those voters are concentrated in urban areas, where roads have been cleared and it will be easier for them to get to a caucus site. It’s unclear which factor will matter more in her fight with Mr. DeSantis for second place.

“If you put a gun in my head right now, I would probably rather be Nikki Haley because she has had the better trajectory than DeSantis over time,” said Mr. Kochel, the political strategist, referring to the battle for second place. “But boy, I wouldn’t bet a mortgage payment on it right now.”

Reporting was contributed by Jazmine Ulloa, Reid J. Epstein, Kellen Browning and Lisa Lerer.