"I'm no expert, but I've heard that once you start sliding down a steep snow slope, you can build up to rocket speed almost instantaneously,"
It depends on the texture of the snow, Robert. If the snow is soft, or at least not brittle hard(what we used to call styrofoam), you have a lot more time to achieve a good self arrest. If the snow is styrofoam, or you're on ice, you've got one chance to quickly set that pick and stop yourself because in a matter of seconds you'll be going so fast that even if you do manage to set the pick, the ice ax will be ripped out of your hands and you will probably suffer a dislocated shoulder when the tether goes taut. Depending on the length of the slope and the run out, that may well be the least of your worries. When I was climbing, the axiom was simply: Don't fall. If you're roped up as part of a team, things are still pretty sketchy on steep, hard snow, or ice. Everything depends on your partner going into solid self arrest very quickly, before he/she get pulled off balance and joins the ride.
Edited to include: Another thing to remember is that in the real world you will be wearing a pack, which complicates things considerably. It is not so easy to do the moves required to align yourself face up, on your belly, with 15, 20, 25# on your back. So practicw with your pack on, if for no other reason than to learn what you'll be dealing with in the field. At that point the reason for the axiom "don't fall" becomes even clearer.