How cold can a brining turkey get before freezing?
Short answer: a recommended 6% brine solution will not quite freeze at 26F.

Long answer:

You should have just looked at the chart on the Wikipedia page, which has % by weight.  That's easy to calculate; just divide the weight of the salt (4.5oz for 1/2 cup) into the weight of the water (133 oz).  This is, of course, way easier to do in metric (128g into 4000g).

Note that you will find widely varying estimates for the weight of a half-cup of kosher salt on the web, from 2.5oz/70g up to 5oz/140g.  Based on weighing Diamond Crystal Kosher Salt in my own kitchen, the correct answer is towards the high end of this range (4.5oz / 128g).  To answer the math part of your question, if you're willing to believe my scale rather than getting out one of your own, each 1/2 cup of salt per gallon represents about 3% salinity by weight and about 3.5deg F drop in freezing temperature, at least up to 2 cups.  

You also should have read better instructions on brining a turkey, as the amounts you ask about, 1/2 cup salt per gallon of water, is far too low in salt.  That's only about 3% to 3.5%, which is well below the recommended brine strength and will result in a watery turkey (as well as frozen brine at 26F).  You want a 6% saline solution by weight.

And, coincidentally, per the chart a 6% brine solution should freeze at around 25F, putting you in the clear.  Mind you, that means you'd better be pretty confident in that weather forecast.

On the other hand, maybe you should try a dry brine instead?