You can definitely climb mountains in Hawaii and that is one of the big tourist attractions. It is not advisable to climb volcanic ones that are active though. People love to experience the mountains by climbing them for the thrill of climbing but also for the beauty on the way up and for the view below once they get to the top.
If you want to really do it big, you can go up Mauna Kea, the worlds's tallest mountain of 14,000 almost. It is a dormant volcano to top it all off. There are certain mountains you are allowed to climb and certain ones you are not allowed to climb so you will want to find out which is which before embarking on a climb. Always go prepared too. Never forget to bring along first aid and water and to let people know the route you are planning to take and when you are leaving and when you expect to return. You can run into trouble and even die if you are not prepared for the journey.
You can also get a guide to accompany your which, having hiked up Mauna Kea, i highly advise.For those who are physically and mentally up for the challenge, mountain climbing in Hawaii is like no other place. I would rather climb in Hawaii than in some really cold place like Tibet. To each his own climb though. Godspeed on your journey.
Yes, you can climb volcanic mountains in Hawaii. Thre's an exciting 11 mile hike around the rim of Kilauea where you will see many natural features. Mauna Kea is the highest point in Hawaii, its steep grade of volcanic stones as well as the thin air because of the high altitude makes this a challenging trek.