I would go light. Try some well built trail runners, there are many with goretex that are waterproof. If not try beefier low cut shoes like the very sticky Five Ten (5.10) Exum Guides or Camp Fours. I have not been to NH in many years but from what I recall many of the higher mountains are full of rocks so sticky lighter weight shoes are better rather than heavy boots with durable soles that are downright slick on wet rocks and really made for packed trails only.
For snow its another story. Since the snow provides quite a bit of cushioning one can use a Mountaineering Boot. (either double or insulated leather)
Sneakyracer's got a point about hard, stiff soles not being great on wet rocks (they're also less comfortable to walk in), but the boots you got are not nearly as heavy or stiff as others, not a bad choice at all. Walk around in them a bit so you get comfortable with them and avoid blisters, that's much more important than the formulation of the rubber in the sole.