I absolutely know NaOH will crystallize out if the solution gets cold enough. My advice is this -- to store NaOH solution from 30% to 50% lye concentration, it should stay above 60F / 15C to keep the NaOH in a fully liquid state. I normally bump that a little warmer -- to 65F / 17C -- to encourage people to stay on the safe side.
What happens when an NaOH solution is at or below freezing -- The liquid thickens into a clear thick gel and will begin to form crystals if the temp is low enough. If the NaOH is kept at or below its freezing temp for a long enough time, some of the NaOH crystals will settle and form a solid layer on the bottom of the container. The process is the same as that for making rock candy --
Have Fun Watching Rock Candy Grow in Your Kitchen
I believe what Orla is talking about is a short-term freeze. In this case, crystals will still form, but if the NaOH solution is used relatively soon after freezing, the crystals might stay small and might not form a solid mass. I haven't tried it to know this for certain, however, so remember this advice is worth exactly what you paid for it.
I'm gonna get on my safety soapbox for a moment --
I will not ever use my food refrigerator or freezer for storing NaOH solution, saponifying soap, or other hazardous chemicals. People need to really think about the possible consequences before they do this. Even if you label the stuff with a skull and crossbones or whatever, you're still creating a serious hazard that has the potential to change a person's life forever.
I have worked as a lab technician in industrial chemistry labs. One rule drilled into chem lab personnel is you never store lab chemicals in a refrigerator or freezer intended for food. And vice versa -- no food in the chem lab fridge/freezer. It's a good practice to follow in a chem lab and an even better rule to follow in the home.