Salt works to reduce the freezing temperature of water. If the freezing temperature is lower, the ice is more likely to melt back into liquid water at much colder temperatures. If it's too cold outside, however, the salt won't work nearly as well.
We set out to test this inside the house by taking two ice cubes from the freezer of equal size. We placed the cubes on a plate and sprinkled table salt on one and then waited for them to melt. My daughter's initial hypothesis is that the cube with salt on it would melt faster. A reasonable hypothesis knowing that salt melts ice outside. Here are a few pictures of our ice cubes melting.
As the ice cube without salt melted, the edges remained smooth and curved, whereas the salt gouge out divots as the cube melted. The ice cube without the salt melted first, but it's possible the cubes started out with different masses. Even then, the ice cubes are not melting due to salt. The temperature inside the house is much higher than the freezing point of water, so the cubes are going to melt regardless. Still, it's easy to see that the salt changes the shape of the cube as it melts.
This is a neat little experiment to test something my daughter recognized was taking place outside to clear sidewalks.