Here is some google info for Alaska and ATVs.
http://www.dps.state.ak.us/pio/releases/resources/Brochures/ATV%20Statute.pdfhttp://www.dps.state.ak.us/pio/releases/resources/Brochures/ATV%20Driver%27s%20Guide.pdfBasic message appears to be not on public roads.
I have seen some out on the Petersville Road and up by Eureka Lodge on the Glenn Hwy east of Palmer in the past. They were just not real popular when I was living in the rural areas of Alaska. Snow machines were very popular, and dog teams for winter travel. I owned one of the 3 wheeler Honda Big Reds for a couple of years before moving south to Colorado.
I really doubt most of the campgrounds are going to allow them to be riden in the CG, be it private, state or federal ones. If it is easy to take along, then take it but I wouldn't make much extra effort to have one with me in the north country unless there was some specific trail or area I wanted to explore more thoroughly. The 40 Mile and 60 mile mining areas being some that pop to mind. 40 in Alaska, up toward Eagle/Chicken and the 60 is in Canada on the road between Dawson Town and the border on the Top of the World Hwy.
Just keep in mind it can be a long walk back if you have any problems. Just like bush flying or 4 wheeling. We used to say the main different in getting stuck or breaking down, in a 2 wheel drive vehicle and a 4 wheel drive one, was with the 4 wheel drive one you had twice as far to walk back. LOL
If you or anyone takes an ORV with you, check with the locals, dealers, clubs, lodges, etc about the places they recommend you go. I used to average about 5,000 miles a year on snow machines, the ones with working odometers and seldom went too far out of town solo. With longer trips, there would usually be 4 or 5 machines and we always took one empty freight type sled with us. It was a rare trip that one of the rigs didn't return home, on the sled, as something had broken on it. LOL