lol.. that wasnt even the 2nd law of thermodynamics wasnt it ..,
anyway, they use salt on ice for making ice cream too, when you need to have an extremely fast drop in temp to solidify the cream. It just speeds up the transfer of heat from the coke(warm) into the ice bath(cold) because the ice with salt just lowers the specific heat so it takes less time for the same energy to heat or cool down the ice bath. basically water has pretty high specific heat so it takes a little longer for it to to absorb the heat from coke.
i think the temp of the ice should pretty much be the same but its all about the time it takes to transfer-absorb heat better which is what allthe dilio is about. it feels colder because it heat from your body gets trasnfered to ice bath in less time so you lose more heat in the same time period as you would with regular ice