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Snow is water, and the salt dissolves in it, which in turn lowers the freezing point. Hence, it melts the snow.
Usually snow melts at 0 degrees centigrade and above. Adding an amount of salt will let it melt at -5 degrees centigrade (for example). The freezing point depends on the concentration of salt in the water: more salt = lower freezing point, less salt = higher freezing point.
As the salt is only on the top layer, it melts the snow at the top layer, which then starts sipping down the snow underneath it. This is a water-salt solution which is sipping down and mixing with the snow that is underneath. Hence, the water-salt solution it is mixed with more water, lowering the concentration of salt. Less salt = higher freezing point = the water freezes again.
The end result is that the snow underneath is more compact and more icy.