I agree with woodsmensPost that theoratically that works, but if you would use Kelvin in stead of Celsius the answer is different,
0 °F = 255.37 K
255.37 / 2 = 127.69
127.69 K = -229.84 °F (And this would be a very simplified and wrong way to calculate this)
I know that is extremely cold but there is no good reason to use Celsius over Kelvin, I don't think you can just take another scale and use it to convert the temperature. Next to that colder is a vague term.
Nice question but I don't think the answer is simple..