In a word...   Yes!
The low air situation causes the tire to "squish" and actually "bow" the
tread...
I mean that if you could look at a cut-away section of your tire, if you
kept the same weight
on your tire, and allowed it to drop in air pressure, you would see the tire
"fatten" out to the
sides but would also see the "footprint" or "tread" of the tire begin to bow
with the middle of
the tread begin to lift off the ground.
This results in a loss of traction.  IE...
Keep your tires properly inflated!
Hths!

just an aside: winter tires is like having a sponge on each corner of
your car. all season tires is like having hockey pucks on each corner
of your car. which slides furthur? the hockey puck.

Yes, the tire becomes fatter and softer so it can float on top of the
snow easier.  This causes steering loss also on the road.

Off roaders use this 'feature' to allow their tires to purposely float
over the snow and mud for slow speed driving.  They also have special
tires with really aggressive edges to still have some bite when running
low air pressure.

A fully inflated tire cuts through the snow usually increasing traction.

Mike
86/00 CJ7 Laredo, 33x9.5 BFG Muds, 'glass nose to tail in '00
'New' frame in the works for '08.  Some Canadian Bush Trip and Build
Photos: http://mikeromainjeeptrips.shutterfly.com

Tire rack has an informative page on this subject...
http://www.tirerack.com/tires/tiretech/techpage.jsp?techid=3