When driving a front wheel drive car when the back end gets loose and fish tails there isn’t too much you can do. First, ease off the gas just a bit as you turn the wheels in the direction of the skid. The idea is to keep the front wheels in front of the rear ones. Don’t overreact and turn the steering wheel only a little and do it gently. What happened to you is you moved the steering wheel too far and the back end came around past center and you were skidding on the other side.
My guess is you were going a bit too fast as you hit a patch of deep, slushy snow. This can slow the front wheels and put the back wheels into a skid. If this happens again it is your signal to slow down after you get the skid under control.