You said it yourself in your first reply - it makes the ice melt earlier. The relevant concept is Gibbs free energy, where endo/exothermic is only part of the equation.

The only reason ice melts at 0 degrees in pure water is that that's the point where the gain in entropy from turning into a liquid balances out the increase in potential energy from turning into a liquid.

When you add salt to the water, you change the entropy part, making it more entropic to melt, which decreases the equilibrium temperature at which ice turns into water. The ice will melt faster when surrounded by salt, absorbing energy (and quite a bit of it! 334 J/g) until it hits the new depressed equilibrium temperature. Then it'll maintain that temperature by melting slowly, just like ice in pure water.