In liquid, the molecules and ions are located in a random manner, are miscible in a wide range of concentrations and move rapidly about.
In crystals, they are stuck, and are stuck in a long range order.
If you cool a saturated saltwater solution - yes, Na+ and Cl- will forsake the solution, break off from all hydration water they have in solution and form dry, cubic NaCl crystals, as long as the temperature is above about 0 degrees.
When the temperature is below that temperature, NaCl starts to form a crystal hydrate - NaCl·2H2O. This is a substance with definite composition based on small integers, definite crystal shape and definite long-range order inside the crystal. It is just a different order than the one inside NaCl or in ice crystals.
If you grow NaCl·2H2O crystals then you can put them to X-ray diffraction or neutron diffraction machines (provided you do not warm them over 0 degrees, where they would incongruently melt and be thereby destroyed) and find out where specifically the H2O molecules exist in every unit cell, and where their protons are relative to the neighbouring O, Na and Cl nuclei.
Now, yes, neutral lioquid water can autodissociate, about 1 molecule out of 5 millions. Ice cannot because OH- ion would not fit in the crystal long range order and ice does not have an unit cell of 5 million molecules. An OH- ion would be a crystal defect, so it is rejected by crystal growth, concentrated in the remaining water, then neutralized by some H3O+ ion also concentrated there.
If you freeze, say, HCl, then you can form crystal hydrates HCl·6H2O, HCl·3H2O, HCl·2H2O and HCl·H2O. HCl is a strong acid, and in aqueous solutions nearly completely dissociated into Cl- and H3O-. Does this mean that the crystal hydrate should because of its long-range order be 100 % dissociated, because the crystal structure would be Cl-·H3O+·5H2O - that any undissociated HCl in solution will dissociate on freezing because an HCl molecule would be a crystal defect? And can you examine a HCl·6H2O crystal by x-ray and neutron diffraction and NMR of the 19 protons and the 6 O-17 nuclei in the unit cell to verify the bond lengths and find out which of the 6 oxygens in in H3O+ ion rather than a H2O molecule?