If you're over 45 and given the choice between a slow painful death and snowboarding lessons, I highly recommend elbow pads. I came up with this on my own, using a pair of $30 hockey pads. I am typing now only because of those pads.
True, it takes some serious geekiness and a rock solid ego to wear elbow pads over your snow jacket, but a hockey jersey makes it look even weirder. I recommend both.
The pads have not only saved my elbows, but they make it much easier for me to fall on my forearms and protect my wrists. They even reduce impact force transmitted to the humerus, thereby sparing my shoulders a bit.
I was proud of my own invention, until it occurred to me that someone else must have thought of this. Google revealed you can buy official snowboarding elbow pads. Hmmphh. These are puny compared to my hockey pads -- they do nothing to pad the forearm. Forget these and buy the hockey gear.
Update 1/28/07: After, or even before, the repetitive falls on icy snow produce disabling back pain, consider Crash Pads 2600 power underwear.