Donald J. Trump has the backing of 48 percent of likely caucusgoers ahead of Monday’s election, a commanding lead for the former president, according to the Iowa Poll by The Des Moines Register, NBC News and Mediacom.

Nikki Haley is narrowly leading the battle for second place over Gov. Ron DeSantis of Florida, 20 percent to 16 percent, according to the survey, which was released on Saturday evening.

The poll shows Ms. Haley, the former United Nations ambassador, improving compared with December and Mr. Trump slipping — but only marginally. He enjoys a 28-point lead, compared with a 32-point advantage last month.

The survey, which has taken on an almost mythic status in some political circles, immediately forms the new base line of expectations for the caucuses on Monday. All three leading candidates have been not just fighting to win the most votes in recent days but also to dampen how well they are expected to perform in order to claim a stronger-than-expected showing.

No other candidate was above single digits, with Vivek Ramaswamy, a businessman who has aligned himself with Mr. Trump and campaigned heavily in Iowa, at 8 percent.

The poll — conducted by J. Ann Selzer from Jan. 7 to 12, with a margin of error of 3.7 percentage points — comes during an unusual cold snap even for Iowa.

The weather has made turnout predictions on Monday especially volatile. The Trump, DeSantis and Haley campaigns have been studying the impact of the storm for any potential advantage, with unaligned political strategists calling the cold — with subzero highs for the day — an unusual test of both natural enthusiasm and organizational might in the race’s final days.

“You have the worst weather, I guess, in recorded history, but maybe that’s good, because our people are more committed than anybody else,” Mr. Trump said in a video announcing that he was canceling some of his weekend’s events.

In the previous Iowa Poll, in December, Mr. Trump was the first choice of a 51 percent majority of likely caucusgoers, and leading among every demographic group. He was dominating by an even wider margin among first-time caucusgoers, with 63 percent support.

Mr. Trump had grown from 42 percent in August, 43 percent in October and 51 percent in December.

Mr. DeSantis had previously stayed relatively steady: 19 percent in August, 16 percent in October and then 19 percent again in December.

Ms. Haley began far behind, with 6 percent in August. Then she rose to 16 percent in October and stayed at 16 percent in December.