Alaska with its frozen tundra will provide a lot of great ATVing. There are two National Forests in Alaska. The Chugach National Forest located in Anchorage no longer allows ATV use on their trails as they are very deteriorated, however you may ride snowmobiles in the area before February 16th and after April 30th of each year.
Tongass is the other National Forest Located in Ketchikan, Alaska and they have designated a good number of trails exclusively for OHV and ATV use. Be sure to stay on the trails, a lot of the area was eroded over the years from people not being aware and responsible when riding their ATVs and OHVs on the land. As with all National Forest Lands, be sure that you have your noise muffler installed and your spark arrestor in place before you ride. There are three kinds of bears as well located in this national forest, be aware when you ride these forest lands at all times.
If you're looking for some good ATV clubs to join in Alaska, check out the Alaska ATV Club website is located at https://www.alaskaatvclub.org and they are located in South Central Alaska but all Alaskan OHVers are welcome. They make safety a top priority and share information on various trails for the best information on riding in Alaska available.
Alaska doesn't have a lot of restrictions on ATVers. However all riders must be a minimum of 14-years old and all ATV riders must wear a DOT approved helmet when operating their vehicle at all times.