Just to add a thought about the abrasive property of snow. My rule is
that if you might need to use your axe to self arrest, you should have
gloves/mittens on. It is terribly uncomfortable to try and arrest without
some hand protection on even a mild slope, hands go numb quite quickly.
Trying to stop on a steep slope without gloves will most likely tear your hands
up and cause you to lose your axe.
I have seen bare hands after somebody tried to arrest without gloves (we
get a lot of ice axe practice here in the Pacific Northwest) on a steep
slope. While the person did not lose their axe, their hands looked
awful.
One last note (this may have already been said, but I will repeat). It is
almost impossible to stop on ice, so don't fall. If you do fall, you must
try and stop the instance you hit the ground (unlikely, since most falls are
unexpected) so as to not gain ANY speed. If you get going on ice, you most
likely will keep going until you come to a cliff, flat spot, tree, etc., but
keep trying to arrest. Never stop fighting, it could mean your life.
You MIGHT get lucky and succeed in arresting.