There is no problem with two strokes up here. We don't have a sticker program or anything like that. If you are looking to make the bike street legal I don't see a problem with that either. Actually the Arctic Cat/Suzuki dealer in Anchorage had a brand new, dual sported RMX on their showroom floor a couple of years ago. They did the conversion so I would have to assume it was completely legal to license.
Alaska is a great place to have a dirt bike. The riding season is shorter than most parts of the country but you can ride until 10:00 or 11:00 at night in May, June, and July. That helps to make up for it.