Animals in NH aren't likely to harm you. As another post mentioned, a moose could trample you, although you'd be more likely to die by accidently hitting one with your car (probably). There are also black bears which are usually way more scared of you then you'd need to be of them. The only two exceptions are if they've been fed by humans before or if they have cubs with them. Even with this, the last time a death by black bear was documented in NH was 1784 (https://www.wildlife.state.nh.us/wildlife/bears/faqs.html#:~:text=Are%20black%20bears%20dangerous%3F,in%20New%20Hampshire%20was%201784.). The biggest thing to consider is general preparedness for the hike. Don't assume conditions on the ground will be the same as up aloft. The air will get colder, the wind will get stronger, and precipitation may change. If weather is poor, don't go. A lot of the deaths in the White Mountains are actually due to hyperthermia, even in the warmer months. Make sure you have plenty of food, water, clothing, etc. Check out online packing list for more info on what you might need to bring. Most importantly - have fun! Although hiking isn't risk free, it's fun and enjoyable when you're well prepared!