In short, learn how to fall.
That, and have no fear. Fear will stop you getting better at trusting your balance, and the rigidity your body goes into when scared helps none in both the falling and not damaging, and boarding well stakes.
I don't have any experience on the snow though. Sadly. Some day I will get round to snow boarding, as I love the look of it. Closest I've gotten was mountain boarding, which was terrifying - speed and not snow... Hmmmm...
Unfortunately I have done the foll on face plant, but on concrete. 'tis the nature of my stupidity though, to pick a past time that aims to maim.