Seriously? No, not at all. At some point early on, if you have a good instructor, you will learn how to fall without hurting yourself (hint: you want to fall in a way to distribute your weight as much as possible. You do NOT want to take all your falling weight on one knee, one hand, one elbow, that sort of thing. Spread the force is the key.)
Then you learn the snowplow, which is stable as can be, and gradually move toward putting your skis together in parallel.
I skied for about 20 years, and only ever had one serious fall that hurt my knee. (See note above about not wanting to take all the weight on one knee...) Nothing broken, ever. There is no feeling like skiing in all the world. Closest thing you can get to flying while still having both feet (mostly) on the ground. I really loved it.
Apologies to OP for hijacking thread...