Neither state has their population uniformly distributed. New Hampshire has a lack of informally established spots out there to shoot for several reasons distinct from raw population density. Idaho has nearly 10x the land area of NH, is much less forested, etc.I just checked the 2010 census. Idaho is listed as the 44th most densely populated state in the U.S., with an average 19 people per sq mile. This might have something to do with the ease with which you were able to find a place to shoot out there. By comparison, this same census pegged NH with a per-square-mile average of 147 people, or 20th most densely populated U.S. state.a lot of informally established spots out there to shoot.
I'm in S.NH and when I open the windows on a sunny Saturday morning I hear gunshots from multiple directions -- mostly people on their own property, but I'm pretty sure there's at least one informally established sandpit in-the-know locals use.