The commercial temperature range for electronic components is 0 °C to 70 °C, industrial −40 °C to 85 °C and military −55 °C to 125 °C. So what happens if you take parts beyond these ranges? Do they fail immediately? Usually not. It is very much component dependent. Some components are quite resilient to very low temperature.
Components generally degrade gradually over temperatures, but after some temperature, some might exhibit large changes and some might fall apart completely. There are some reasons for these abrupt changes. For instance, a gate driver stops working completely below -120C because the logic threshold increases too much and the input fails to trigger. One voltage regulator falls apart after -130C and another regulator with similar specifications holds up well at -150C; this can be attributed to some small design differences in the current limit and thermal limit circuitry. The SRAM based FPGA can fail in an unpredictable and dangerous way. As the temperature goes below -125C, the increase in transistor threshold can cause the SRAM bits that hold the logic configuration to flip which could completely alter the logic output.
There is no good way of knowing which part might do better at low temperatures other than testing and screening.