Each year (since 2000) they open the Mt Washington auto road for ATV and UTV access, calling it the Gerry Pomerleau Memorial Ride in honor of the late director of the New Hampshire ATV club.
https://mt-washington.com/events/nh-atv-day
Our first time attending was this one, in June 2017. If I remember correctly, tickets go on sale in January each year and sell out very quickly.
The ride was a fun way to go up the mountain and is very popular, even though the weather at the top is often very uncooperative.
The video is kind of long (5 min or so) and includes footage from the whole trip. The embedded player/link on this page starts at the beginning of the Mt Washington but of course you can rewind to catch the other parts as well if wish.