I regularly drive my 2003 Honda CR-V AWD on forest roads here in New Mexico. There isn't much gravel anywhere, generally it is graded dirt and rocks. Some roads haven't seen any work in a year or two, sometimes more, but we don't get nearly as much rain as NH. If it is dry, the real issue is ground clearance, which is pretty good in my CR-V - you just have to pick your way around the biggest bits.
The most exciting trip I did was with a group to go caving in the Malpais, south of Grants, NM. This was in the spring, so the snow had melted, but the Malpais doesn't drain well, being a thin skin of dirt over the lava flows. So, the roads were all mud (several inches). One car in the group was FWD only, and it had to be towed through the worst because once the rear wheels started sliding sideways it would end up in the ditch. When we encountered meadows they were covered in standing water, and you had to pick a line across the meadow and go for it, not knowing really what was under it. On one meadow I was unlucky and managed to bounce down on a rock at some point, which took out my evap filter (which I had to get fixed later). At one point, one of our 4WD F-350's got bogged down and had to get towed out - it was that messy of a road. I'd say the CR-V performed very well.
All in all, I've been very happy with the CR-V and regularly take it down pretty nasty forest roads. I'm not sure that I'd take it 'off road', i.e. where there is no road at all. I have friends who do serious off-roading events, and my CR-V is certainly not suitable for that.
Take a tire pump and repair kit. A winch isn't a bad idea either.