We have M+S (Michelin LTX M/S) tires on the RX too and trust me, the grip level is no where near a true snow/winter tire. Having been in friends' cars with true winter tires, I can honestly say they'd run circles around my car in snow/icy conditions.
The thickness of the snow/ice doesn't matter when you're skidding on ice. Ice is ice. Unfortunately, VSC, AWD, snow mode, and all the other technology in the world won't help you if the tires themselves have no grip. :(