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Are you sure that you have four-wheel drive? The ECT snow button as I recall was only used on the 2 WD model. This button is designed to start the transmission off in second gear instead of first gear thereby decreasing the chance of wheels spin on slippery conditions due to higher gear range providing less torque. The four-wheel drive models had a button there that says Lock which allowed you to lock the center differential to provide better traction control. If you have the vehicle identification number handy I may be able to cross-reference to find out exactly which transmissions this car has two or 4WD.
Having the vehicle in park would be the best way to go but yes if you push the snow button this will give you less chance of breaking the wheels loose because the transmission will start in second gear instead of of first gear which provides for a more sluggish acceleration. The light will illuminate on the panel that has Snow.