The conventional wisdom is that New Hampshire is a fairly libertarian place. With Trump, Kaisch, and Christie outpolling both Republican Liberty Caucus candidates in Cruz and Paul in New Hampshire it appears that conventional wisdom is incorrect. Is it regional bias (Cruz and Paul being Southerners) or something else?
The state motto is "Live Free or Die". New Hampshire does not have an income tax on wage income nor a sales tax, so traditionally has relied on property taxes to provide services at the local level. With a relative small population it doesn't need or can't afford a massive state bureaucracy. You can't rail against the politicians "up in Concord" and be taken seriously. If you were from Massachusetts or New York, you would probably regard New Hampshire as libertarian.
There was an effort a few years ago to get a group of Libertarians to move to New Hampshire, with an effort to take over the state politically. You might reason that a cadre of 50,000 persons might be able to take over the state. But if you have a cadre taking over a state it will disintegrate into folks fighting for power. Most people need a job to live somewhere, and I don't think that many people moved.
Techies in Nashua and Manchester may have interest in Libertarian values, but they might not be willing to go without state schools for their children. And even if they did, their neighbors don't. And Boston has too much influence over the state.
This is pretty accurate, I'd say.