I think it's all relative to the terrain where you hunt. I hunt near Kirkland Lake Ontario and last year I shot a cow. Wasn't a terribly big cow but she was alright size. What we do is gut the moose at the kill site, tag it then tie the head to the back of the 4-wheeler and drag it out whole because that how we hang it in the garage. I shot the moose 1.5 km from the road where the truck and trailer were, I was using my uncles 2008 Grizzly 660 with aggresive tires and it took us right around the 2 hour mark to cover the 1.5km. So have a look at the area where you're hunting. I would think that a 350cc-400cc would be good enough on gas for trails but can also be a work horse for you when you need it.
My dad has an older Grizzly 600cc (98 I think) and once I learned it's capabilities, I can get pretty much anywhere I want.
PS- If you hunt where there's mud, get a winch. You never realize how valuable it is until you have a 600lbs 4 wheeler, a moose tied to the back, and none of it is going anywhere.
My dream quad is a Grizzly 700FI in the Camo body kit
X2 on the 2008 Grizz 660, have one. Friend has the 700, guess what? the 660 is better, why? 700 doesnt have pull cord,doesnt have stainless exhaust, is only like 18cc's bigger "not a real 700"
One fellow made a good point on here suggesting the smaller bikes, I also have a 2005 Kodiak, it is a bit smaller size wise then the Grizzly but still has more then enough power to pull a moose.
I strongly, and I mean strongly advise against getting one of those Canadian Tire ATV's, they are junk, and when I say junk I mean junk. Spend the money and get a real bike.
I realize everyone has their own opinions on what ATV brand is the best, but if you do some honest research you will find in the end Yamaha wins hands down. Hondas are ok but no comparision to the power, suspension etc that Yamaha has. CanAm is ok too but I hear they are making them in mexico now.
Good luck getting yourself a nice ATV.
PS for the guy I am quoting. I am just outside of KL
ETA: Also, after you buy your ATV, GET A WINCH! and get the BEST. Get a good Warn winch, yes they are expensive but they will never ever let you down. And if you can afford it get one for the rear of the bike as well.