When you dissolve a "salt" (the whole class of them, rather than just NaCl), there is a lattice energy (you are tearing these crystals apart) and a hydration energy, which are a little give and take from an energy standpoint. Most salts dissolving are slightly exothermic. NaCl dissolving is very slightly endothermic.

Seawater? Well, remember, there's a lot of dissolved solids in there, not just salts. So you have a summation of dissolving a whole menagerie of different things into your water. Last I heard, and it's been many years since I went near anything like that, yes, there's both an entropy and an energy cost, although I would personally dread trying to do calorimeter measurements to verify it experimentally.