I would also think that it would be illeagle to hunt a big game animal from a snowmobile as well as unethical.  I don't know the exact verbage cause I don't have the regs in front of me but I've read that "pursuing game from vehicle (plane, helicopter, motorcycle, etc.)  is not legal.  Not to mention that irregardless if it was a hunting season or not, chasing elk in "4 ft. of powder just to get a look at them" can exhaust an animal that is already basically starving and worn down.  Now they would become susceptible to cougars, coyotes, poachers, whatever.  Mature bull elk lose a lot of their fat reserves after the rut is over, and only have a limited amount of time to gain some of that back before the winter snow covers much of the feed.  Bad idea!