A word of caution: NH has probably the most diverse and complex road law of any state. In many cases different attorneys with experience with road law will disagree on a specific “road”. I would not depend on the opinion of any specific town official as to the status of an older private road.
Newer subdivisions often have clear road ownership. Local planning boards normally require the road be built to town standards and dedicated to public use. The developer retains title until enough lots are sold for the town to take title to the road. Other new subdivisions may have a private road planned with common ownership of such along with any common land. The HOA agreement, as recorded, would spell this out. Not necessarily true for older subdivisions.
Try downloading a copy of the New Hampshire Municipal Association handbook here:
https://www.nhmunicipal.org/sites/de..._to_travel.pdf
Alan