If you go into a turn fast and try to accelerate more, then ESP would kick in and bog down the car as it cuts fuel and prevent the car from accelerating. If you go into a turn slower and floor the gas from there, ESP would kick in but most of what it does would be inner wheel braking but not cut the fuel, so you still feel the acceleration out of the corner.
I would leave ESP on, especially in the wet or snow. Even with all 4 wheels being driven in a turn, the car might still plow forward depending on if it is slipping, what the momentum of the car was, how much gas you are applying and whether you are in a low gear, which would apply more torque to the wheels. Sometimes it might plow forward, other times it might do some 4 wheel drift.