Sweden, Norway and Finland (Fennoscandia) are at roughly the same latitude that Alaska, The Yukon, and the North-Worst Territories are - perhaps a trivial bit more southerly - but even a fleeting glance will reveal that the area is fairly different from North American areas of the same latitude. There's considerably more broad leaf plants, there are quite a few pines (I'm not sure, but I think there are no pine species in AK), and the average temperature is quite a bit warmer. I'm no climatologist, but I've been told it's because of a warm ocean current that pushes up into that area, moderating the effect of the arctic. I could be mistaken, though.
From the perspective of game, there is a huge difference. A good estimate is that in the whole state of AK, about
Scott Brainerd, now at ADF&G, but a guy we stole from Norway (sorry Norway!), had been talking to us about how this just doesn't seem likely. First, you have the productivity issue (the milder seasons, more plant growth, and favourable soil) which leads to a big difference in biomass between similar North American regions and Fennoscandian regions. Biomass is literally just that - the mass (weight) of biological stuff.
Second, Scandinavia has some very intensive forestry practices, which involve quite a bit of timber harvest. While timberharvest isn't great for many species, it tends to be very good for moose in a short period, as it creates a bloom of new second growth. This might not be sustainable in Scandinavia, and I've heard a few people mention that the good times won't always roll - that they're headed for a crash. Alaska doesn't have that sort of timber available to harvest in moose-relevent areas.
Third, access in that whole region is phenomenal. There is few areas in Norway or Sweden that you can't reach quickly through road and off-road vehicle access. They have about a 700 year head start on building roads. You can see a clip of the end effect in that picture to the right. I don't think there's any place where you can go 30km straight line and not intersect a road of some sort.
Predators are all but expatriated. Wolves were quite actively hunted (over-exploited in most areas) until 1976, when hunting and trapping was restricted. Wolf numbers remain very low, as do brown bears. As I mentioned before, Arctic Fox are also in a bad situation.
Finally, hunting itself is very different in Fennoscandian, compared to Alaska. This is far too big of a topic to go into with any coverage here, but in a nutshell, animals are owned by landowners, not the state, hunting is typically done in territories and by teams, as opposed to family units in an ad-hoc manner, and moose meat is commercially viable, whereas sale is restricted in Alaska, Yukon, etc.
Scott said the question shouldn't be `can we do it?`, but instead `would we even want to?` The factors that make the difference in moose numbers are fairly serious, and while we could make a best effort at copying the Fennoscandian model, the end effect looks mildly unpleasant for the United States and Canada.