You're not strapped to them; they have quick-release bindings which are set pretty loose for beginners, so the skis snap off and can go flying away on their own when you crash.
And yeah, snow is soft. Unless you go out in the early morning and it's icy.....I faceplanted into an ice ridge hard enough to smash my sunglasses and give myself a minor nosebleed (plus lost some skin off my nose too) on my secod ski-ing trip.
Snowboards are much more painful to crash with.