The northeastern state, home to just 1.3 million people, sets the tone for the primaries and could shake out a crowded Republican field of candidates pitting Trump and arch-conservative Senator Ted Cruz against more establishment candidates led by Senator Marco Rubio.
Kicking off the primary in a time-honoured tradition, the handful of voters in Dixville Notch, one of three small communities to vote at the turn of midnight, went to the polls.
Sanders took four votes to none for Clinton, while Republican Ohio Governor John Kasich received three to Trump's two.
But everything still remains in play in New Hampshire due to a high number of registered independents, who can choose to vote in either party, along with up to 30 percent of voters who were still undecided in the days before polling.
Snow fell heavily in the state late Monday, snarling traffic and creating a last-minute obstacle for voters and candidates who braved plunging temperatures and freezing winds.
"This is crunch time," the Republican frontrunner Trump told thousands of cheering supporters at an event delayed slightly by snow in Manchester late Monday.
"You have to go out, you have to vote, we have to celebrate tomorrow evening," added Trump, who traded barbs with rival Jeb Bush on the eve of the vote.
"Let's have a big, big victory."
Trump has energized broad swaths of blue-collar Americans, angry about economic difficulties and frustrated at what they see as their country losing its stature in the world. But the New York billionaire will have to translate his soaring lead in the polls into a win in New Hampshire if he is to recover from the embarrassment of finishing second behind Cruz in the Iowa caucuses last week that kicked off the presidential nomination process.
The rest of the Republican pack has been fighting it out, aiming for a strong second or even solid third-place showing that could reinvigorate them for South Carolina and Nevada, the next stops on the long road to becoming the party's nominee.
A poor result will likely rupture the presidential dreams for 2016 for former and current governors Bush, Kasich and Chris Christie.
- 'No perfect candidate' -
On the Democratic front, Clinton will be looking to confound polls that predict her insurgent challenger, Senator Sanders of neighboring Vermont, will gallop to victory in the state. The RealClearPolitics poll average shows the self-described democratic socialist -- who has called for nothing short of a "political revolution" -- leading 53.3 percent to 40.5 percent for Clinton in New Hampshire.
Clinton won Iowa by a hair, but Sanders is keen to show that his campaign, built on economic fairness for all, can give the former secretary of state a run for her money deep into election season.
"For all those of you who are still deciding, still shopping, I hope I can close the deal between now and the time the polls close," Clinton told a rally at a community college on Monday. She also enlisted her husband Bill Clinton as the ultimate campaign surrogate.
The former president has hammered Sanders for his supporters' "sexist" attacks on his wife.
"Not one of the candidates are perfect," said Robbie Grady, a retiree attending a final Clinton rally.
"In my eyes I think she's the most qualified and she's the person I'd like to see in the Oval Office."
- Trading barbs -
Rubio in particular will be hoping to match or better his strong third-place finish in Iowa, despite taking a drubbing in Saturday's debate when New Jersey Governor Christie eviscerated the first-term senator for regurgitating scripted talking points.
Bush, who tangled with Trump at the debate, sharpened his attacks on the real estate tycoon, calling him unfit to be president.
"You aren't just a loser, you're a liar and a whiner," Bush said on Twitter.
Trump shot back that Bush was a "low-energy guy" who "doesn't like my tone."
The former reality TV star also delighted in repeating a woman's insult in the crowd, calling Cruz "a pussy," to laughter.
Brian Carey, who runs a construction company and custom-made a neon Trump sign for his barn in his largely Democratic town, told AFP at the final Trump rally: "You need a businessman to run the country. The country is being destroyed right now." But some say they have become disillusioned with the frontrunner's bombast and arrogance.
"He's got some good ideas, but he's a bit much sometimes," said Joseph, 19, a student.