Is there a temperature where salt doesn't dissolve in water?
Solubility is an equilibrium phenomenon, which means that its temperature dependence is a function only of the enthalpy change of the reaction, not the entropy. See the van't Hoff equation for the mathematical relationship. 

If by salt you mean sodium chloride, the dissolution in that case is only very slightly endothermic, so the solubility decreases very slowly with temperature. 

That means that if you go low enough in temperature, you will reach a point where the solubility theoretically approaches zero. However, the water will freeze long before the temperature gets that low, and solubility will no longer have meaning.