Once you've lost traction and your wheels are locked up, slamming your brakes won't change the situation. What you should do when you feel yourself begin to skid is ease off the accelerator and let the car slow down on its own. A moving tire means that there is still some traction, which is what you need to steer yourself out of a collision.
If braking is required and your vehicle comes with an anti-lock brake system, brake with steady, even pressure. If your car doesn't have ABS, then you should pump the brakes by quickly braking again and again.
When handling snow-covered corners, you should begin a steady braking as you approach the turn. Once in the corner, ease off the brakes and use the car's remaining traction to steer through the turn.