Originally Posted by max-a-mill
on my mtb i always run a WAAAY bigger front tire for increased cornering and bump absroption. no worries at all.
i'd always stick the bigger one on the front. also, the rear tire seems to contribute more to rolling resistance than front tires so having a higher psi smoother tire back there will get you the most performance advantage.
plus as the other poster said, ideally you want your rear tire to wash out before the front. not that you really want either washing out but i hope you get the idea

I did this all winter. 26x1.5 street tire on rear. 26x1.9 knobby on front at low PSI. You don't want to lose traction on the front tire.
Alot of people who have studded tires only use them on the front.
I think most of your weight is on the back wheel. So, it makes sense to use a skinnier high pressure tire without knobbies back there. More efficient. Not much increased danger due to loss of traction. Note, I did have to walk up the big hill once this past winter. Studded tires in back would have helped on that day.
Edit: Looks kind of dorky, though. Guys at work were making fun of my bike with the non-matching tires.