(I'm surprised this question or a very similar one hasn't been asked, so I wouldn't be surprised if I just failed to find a question with my search that does answer this question.)
I dissolved some KX3POX4 in water a while back, and the solution became very hot. I commented on this to my labmate, and he said "So that means it's more soluble at low temperature, right?" I evaded response because I disagreed but didn't have a thought-out response yet.
I think he thought of the reaction as: KX3POX4⟶3KX++POX4X3−+heat
But I think that's missing an important step. I think it's more like this: KX3POX4⟶3KX++POX4X3− POX4X3−+HX2O−⇀↽−HPOX4+OHX−+heat
Phosphoric acid's third pKa is pretty high, so the second reaction is pretty significant. This, I would say, is why this particular reaction is so exothermic. So, in this case, I don't really think the heat plays into the solubility of potassium phosphate.
Sometimes, though, solvation comes with a positive change in temperature. For instance, the enthalpy of solvation of sodium iodide is −7.53 kJ/mol. Sodium iodide, though, is still more soluble at high temperatures. I could be missing something here, though.
In the cases where it is specifically the solvation reaction that causes a temperature change, is it the true that lower temperatures always increase solubility of salts with exothermic solvation reactions (and vice-versa)?
I'd say that the answer is no because the solvation should be dependent on ΔH−TΔS and, since the enthalpy change half of that formula is temperature independent, as T goes up, solvation should be favored by any solvation that has a positive change in entropy. However, I can't really think of any solvation that has a negative change in entropy.