I have hiked in NH in every month of the year. May (especially early May) is probably the worst time of the entire year to hike in the White Mountains which I assume is where you're planning to go. The trails will be a mix of mud and rotten monorail. Personally I don't find it enjoyable and tend to stick to lower elevation hikes like the Belknap range in May but it's doable. Just make sure you have microspikes. They're a must that time of year. Also don't plan on being able to use any of the trails around ravines in the presis. Tuckermans will still certainly be closed.

If possible, I would recommend coming during the summer. August/September are the most pleasant months to hike in NH IMO.