The New Hampshire presidential primary will be held on Jan. 23, 2024, just 8 days after the Iowa caucuses, marking the first primary in the nominating process. What are polls saying about the New Hampshire primary? New Hampshire has an "open" primary, meaning that voters who are not declared with either party can vote in the primary. How does the New Hampshire primary work? A 55-year-old, Michigan native who moved to New Hampshire a year ago, Paige Leary, said she appreciates how involved New Hampshire voters are in the political scene.