You must be a patient that qualifies under certain health conditions that are listed. For prospective buyers from out-of state, you may not go to the dispensaries and buy the marijuana. You may however, possess marijuana but you have to have brought it from another state upon entering New Hampshire.
No, even though there have been considerable efforts to both reduce punishment and decriminalize marijuana, the laws are the same for all people regardless of origin and considered to be rather harsh in that they punish even the smallest possession amounts with fines of up to $2,000 and potential incarceration for up to one year.
All travelers to a state are subject to the laws of that state and Country. In New Hampshire, Marijuana is still legally a class 1 drug and possession of any quantity is illegal. Additionally, driving while under the influence of Marijuana is also illegal. If caught with any amount of Marijuana in New Hampshire, fines could be up to $2,000 and/or up to a year in jail.