Used and loved BF Goodrich All Terrain for many many years on my 4x4 Jeep and a 2 wheel drive Chevy 1500 Truck. Obviously, the 2 wheel drive just cannot hack it in the ice/snow....
....but, my last set of tires for the Jeep were Big 0 Tires brand, Big Foot. The best tires we have ever owned and awesome for traction in the snow/ice. These are also All Terrain.
The maneuverability in rough terrain as well as snow are awesome. I am hooked on these now. I just recently purchased them for my 2500 Chevy Truck and they are wonderful. And much much more quiet than the Mud or Rugged Trail.
Good Luck!