DES MOINES, Iowa — Donald Trump won the Iowa caucuses Monday, a crucial victory at the outset of the Republican primary that reinforces the former president’s bond with his party’s voters even as he faces extraordinary legal challenges that could complicate his bid to return to the White House.

The magnitude of Mr. Trump’s success is still coming into focus, but the former president’s supporters endured a historic and life-threatening cold snap to participate in caucus meetings that unfolded in schools, churches, and community centers across the state.

The results are just the first in what will be a months-long effort for Mr. Trump to secure the GOP nomination a third consecutive time. They send an unmistakable message to the Republican Party, though, that the nomination is Mr. Trump’s to lose and crystalize the challenge facing his GOP opponents.

Ambassador Nikki Haley and Governor DeSantis are Mr. Trump’s most prominent primary rivals. They are aiming for a second-place finish in Iowa that would give them at least some momentum heading into future races.

Both are already pivoting their focus, with Mrs. Haley poised to compete vigorously in New Hampshire, where she hopes to be more successful with the state’s independent voters heading into the January 23 primary.

Mr. DeSantis, meanwhile, is heading straight to South Carolina, a conservative stronghold where the February 24 contest could prove pivotal, before then going to New Hampshire.

Iowa is an uneven predictor of who will ultimately lead Republicans into the general election. President George W. Bush’s 2000 victory was the last time a Republican candidate won in Iowa and went on to become the party’s standard-bearer.

Mr. Trump has spent much of the past year crafting a far more professional organization in Iowa than the relatively haphazard effort he oversaw in 2016, when Senator Cruz carried the caucuses.

His team paid special attention to building a sophisticated digital and data operation to regularly engage with potential supporters and ensure they knew how to participate in the caucuses.

For months, the former president predicated a commanding Iowa victory with a 30- or 40-point blowout that he argued would render the rest of the primary essentially unnecessary.

His aides have privately focused on meeting or beating Senator Dole’s nearly 13-point win in 1988, the largest margin of victory ever in a contested Iowa Republican caucus.

The former president campaigned in Iowa sporadically and largely abandoned the state’s tradition of intimate appearances in living rooms and small community venues.

He instead relied on larger campaign rallies where he more often listed grievances over the past, most notably his claims that the 2020 election was stolen, rather than articulating a detailed vision of the nation’s future.

The challenges confronting Mr. Trump will intensify in the weeks ahead as he balances the demands of a campaign against multiple legal threats.

He has said he will return this week to a New York City courtroom where a jury is poised to consider whether he should pay additional damages to a columnist who last year won a $5 million jury award against Mr. Trump for sex abuse and defamation.

The Supreme Court is weighing whether states have the ability to block Mr. Trump from the ballot for his role in sparking the January 6, 2021, breach of the Capitol. And he’s facing criminal trials in Washington and Atlanta for his alleged efforts to overturn the 2020 election.