The LM317S is only available with a 0 degree lower temperature limit.
It is possible to read right through the datasheet, and be convinced that: a) internally its the same silicon as the TO220 (T) or the TO3 (K), which in some varients can work to -55C (LM117); b) it looks like can be stored over the same temperature range as the other package varients, so presumbly there is no thermal stress related damage that occurs inside devices mounted on a PCB.
However, its not explicit- is the device irreprably damaged below 0 degrees if it gets powered up by accident, or is the situation just, (I suspect) it is not expected to regulate properly and the output voltage is out of spec. We have a design where one of these devices may be powered up after storage in a cold place, and does not have to work below zero, but must recover when it warms up.In our case, given the supply and load on either side, there is no risk of damage, even if the IC passes input straight through to output when cold.
Ideally we don't want to respin the existing board for another regulator - is it possible to advise what is likely to happen ?