Is TRACTION improved if you let some of the air out of the tires, below the recommended pressures?
No. In fact, this is a dangerous practice. Under inflation does not improve traction. It causes the tire to run hot, which can damage it and increase the risk of a blowout. It will also wear out the tread faster and reduce your car's fuel economy. Proper tire pressure information can be found in the vehicle owner's manual and on the tire information placard on the vehicle.