TL;DR: If a firearm is legal for you under Federal law, it's legal in NH
New Hampshire law (regarding possession) makes no reference to barrel length, threading or attachments; if it's legal federally, it's legal in NH.
With very few exceptions, the RSAs around firearms are simple and human-parsable, so you should review them for yourself (Start with RSA 159) instead of taking legal advice from an Internet forum.