Why do we heat salt water to desalinate it rather than freeze it? Most sea water desalination plants rely on the basic principle of heating water to evaporate it, after which the salt-free vapor is condensed. According to Wikipedia, over half the cost of desalination is made up of energy cost, since heating water is very energy intensive. As a back-of-the-envelope estimate, the energy required to bring $1~kg$ of room temperature ($20$°) to a boil under atmospheric pressure is about $620~kcal$. $80~kcal$ to heat it to $100$°C and another $540~kcal$ to bring it to a boil.
Conversely, cooling it down to $0$° takes $20~kcal$ and $80~kcal$ to freeze it, in total $100~kcal$, less than $1/6$ of the energy requirement of the heating method.
This kind of desalination procedure happens in nature - icebergs are largely frozen fresh water. Nevertheless, it seems this is not common in commercial desalination.
Is there a physical reason why freezing water is less suited for desalination compared to heating it?
 A: Looking at a phase diagram for water (this one By Materialscientist - Own work, CC BY-SA 3.0, Link) one sees that, starting below 23.3 wt% NaCl in water and above 0C you have a liquid solution (the oceans are around 3.5 wt% salts, mostly but not all NaCl).

So, what happens as you cool it? Well, the liquid solution cools at that NaCl content in water, until it hits the green line. Cooling further results in formation of ice containing the solubility limit of NaCl in ice. This value is pretty low, so lets assume it is, in fact, pure ice. (Note that other salts in the sea water will have different phase diagrams and solid solubilities in the ice.)
Continuing to cool the sample results in more formation of "pure" ice, leaving an increasingly saline liquid solution, requiring the sample to be cooled further. At some point one finally reaches the eutectic point at about -21.1C and 23.3 wt% NaCl. Cooling further results in formation of a ice/NaCl mixture. No further separation is possible. Now you can unload the chunk of solid, cut off the 'pure' ice, and melt that to use as water. Throw the rest away. 
So, yes, you can use the freeze method (assuming that the resulting ice from real sea water meets your specs) in a batch process. Don't forget in an energy balance that you need to account for cooling of the solution to -20C or so. 
Distillation can be done in a continuous flow process, which (ask a local chemical engineer) is much more desirable as a production method. Note that icebergs are the result of a just such a distillation process, using natural evaporation from oceans and other water sources to ultimately produce snow fall which then generates ice. 
