I've used all manner of rifle calibers up here on just about every critter aside from sheep and goats. I would have no problem using a 30/06 loaded with good bullets for all my big game hunting. Heck I've used a 300 Savage for about 75% of my hunting the last 3 years. My main rifle I think of as my Alaska gun is a 35 Whelen and I own about 25 CF rifles from .17-.45 caliber.
I would sooner use the Whelen or an 06 and have my 17Rem for predators than only have an 06 and my 375 or 458. Big game is easy, but it takes a pretty specialized cartridge to do good work on fox and other fur critters without ruining hides.