The goal of rock salt (NaCl) is to form a brine (a water/salt solution). The lowest temperature that such a brine will not freeze at is around -21º C, which is for a solution with a 23.3% concentration of salt. Solutions with a lower concentration of salt will have a higher freezing point.
So, technically they will work down to that point, however, as it gets colder it takes longer and is more difficult for that brine to actually form, so in practical terms, it becomes fairly ineffective at lower temperatures.
It's impossible to give an exact number because there are so many variables that factor into the process: air temperature, pavement temperature, wetness of the snow, granular size of the salt, etc. The typical point of ineffectiveness I see stated is around -9º C (15º F).
Smaller grain salt is better because it results in greater surface area contact between the salt and ice. Other than that, there are different salts that can be tried. Calcium Chloride for instance can form a brine that won't freeze until -50º C. It is also hygroscopic (water attracting) which helps with brine formation. Some places make a brine and spray that directly on surfaces (or pre-wet their solid material), which is very effective, but I wouldn't know how to do that on one's own.
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