If I brine a turkey in a solution of 1/2 cup of salt per 1 gallon of distilled water, how do I tell how cold it can get before the brine freezes?  Here in America, we all know water freezes at 32 degree Fahrenheit... if pure. Salt reduces the freezing point of water, which is why we salt our roads to melt ice in winter.  Since my fridge is fairly full, I would prefer to keep the brine bucket in the garage overnight. However, it may get as cold as 26 degrees F tonight. Will a brine with 1/2 cup salt per gallon distilled water freeze at that temperature? Is there a good way to calculate the temperature to make an answer applicable to multiple brine ratios and temperatures?  Wikipedia has a page on saline water and its freezing points but this requires calculation of molar masses and more chemistry than I am capable of - is there a way to simplify this in the context of cooking proportions? I.e. cups and gallons, not g/cm3 and other measurements.  To be more specific, I am using Alton Brown's brine recipe. 1 quart of store-bought vegetable stock mixed with one gallon of water, 1 cup of salt, and 1/2 cup of brown sugar. Boil to dissolve/mix, then chill in the fridge. Combine with another gallon of chilled water and store chilled (fridge or outdoors in a cold climate, in a detached garage in my case). However, a good answer will not assume a specific recipe: it will specify ratios and explain "X cups salt, Y cups sugar, Z gallons water = W% brine concentration" since not everyone uses the same brine. I am looking for an answer that anyone can use to convert cooking volumes (cups/gallons) into temperatures: "I put X cups of salt into Y gallons of water, how cold can it get before this freezes and the brine fails to do its job?"    Actual results: the brine appears not to have frozen. When I checked in the morning it was liquid without any ice chunks floating in it. I am still interested in a more scientific approach to planning this, however. 
The tomato paste in your recipe is a large contributor to the sweetness. You could reduce the amount you are using or substitute with tomato sauce.   The addition of an acid would also help balance the sweetness. A splash of vinegar or wine for example. 