Snow button...does two things:
1. Reduces throttle sensitivity. This means that if you slam on the gas pedal, it will purposely open the throttle (butterfly valve in the throttle body) much slower than if you were not in snow mode, resulting in a more controlled acceleration from stop.
2. Raises the AWD-RWD transfer speed. Like many others here, I don't know the EXACT speed at which the ECU tells the TCU to make a RWD powertrain. Again, from what I remember, this number is 19mph. In snow mode, you will maintain the AWD start for higher speeds than if the button was not depressed. The transmission will still be RWD biased and will revert to a RWD, just a little later on.
The '03 models did not have a snow button, but rather an AWD Lock button, which did the same thing except did not have the throttle sensitivity adjust that the snow mode has.
ATTESA E-TS traction system
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Infiniti's advanced Vehicle Dynamic Control (VDC) system with Traction Control System (TCS) is standard on all FX models. VDC adjusts brake pressure and engine torque automatically in understeer, oversteer or slippery road surface situations, helping the driver keep the intended path.
The ATTESA E-TS™ (Advanced Total Traction Engineering System for All Electronic Torque Split) all-wheel drive system utilized on FX45 and FX35 AWD uses an advanced torque split control strategy that automatically transfers optimum torque to the wheels according to road and driving conditions. The system provides outstanding handling due to optimum torque distribution for front and rear SNOW MODE(50:50 up to 0:100). ATTESA E-TS™ also provides high starting traction performance and smooth, stable acceleration, especially in snow-covered or off-road situations with a 50:50 torque split at standing start.