Li-ion cells like almost any other batteries do not like cold temperatures. Low temperature increase their internal resistance and lowers its usable capacity. Li-ion works well in freeze temperatures, they even works in -20°C although their capacity is low and they suffer permanent damage. Prolonged use in cold temperaturs will permanently damage the battery and greatly reduce the available capacity.
In all our closed batterypacks you find li-ion cells Samsung INR18650-35E. Samsung specifies allowable temperature range between - 10°C to 60°C (Operating temperature - discharge), where its functionality is guaranteed. Panasonic, the other top quality manufacturer specifies temperature range down to -20°C. In my own opinion, both batteries works in -20°C and Samsung is just more strict. This is one battery test https://lygte-info.dk/, where danish tester discharged similar cell Samsung INR18650-36G (3350mAh) in the freezer with temperature -21°C and even measured good capacity. Futher evidence includes NASA document Performance and Safety of COTS 18650 Li-ion cells from Various Manufacturers with various Panasonic NCR18650A (3100mAh) tests. You can do your own test in your freezer, common freezer temperature is -18°C.
Some other recent studies tell that li-ion works even in -40°C under low discharging current conditions.
How much is the available capacity lowered? The answer is not easy as the capacity depens also on discharging current. And graphs shows also one interesting behavior when discharging current is very high (e.g. 4 Amps), battery internal resistance heats the cell to the room temperature and keep it.
Panasonic NCR18650GA - discharging current 4A in 0°C, measured capacity is 3080mAh, that is 92.6% of capacity in 25°C. 
Panasonic NCR18650GA - discharging current 4A in -10°C, measured capacity is 2920mAh, that is 88% of capacity in 25°C. 
Panasonic NCR18650B - discharging current 3.3A in 0°C, measured capacity is 2950mAh, that is 90% of capacity in 25°C. 
Panasonic NCR18650B - discharging current 3.3A in -10°C, measured capacity is 2800mAh, that is 85% of capacity in 25°C. 
Panasonic NCR18650B - discharging current 3.3A in -20°C, measured capacity is 2190mAh, that is 67% of capacity in 25°C. 
Panasonic NCR18650A - discharging current 0.62A in 0°C, measured capacity is 2550mAh, that is 86% of capacity in 25°C. 
Panasonic NCR18650A - discharging current 0.62A in -10°C, measured capacity is 2400mAh, that is 80.5% of capacity in 25°C. 
Panasonic NCR18650A - discharging current 0.62A in -20°C, measured capacity is 1400mAh, that is 47% of capacity in 25°C. 
Samsung INR18650-35E - discharging current 3.4A in -10°C, measured capacity is 40% of capacity in 25°C. 
Yes, battery gets permanently damaged when used under 0°C. The lower temperature, the more it would be damaged. When discharging current is low (e.g. C/10 = 0.34A), damage is low. In high discharging currents, damage is significant. Some studies tell that high discharging currents not necessarily damage cells more. However, if the true is anywhere, one clear thing is that under freeze temperature use damages li-ion cell and you should beware such scenario.
Higher damage is caused when charging cells in low temperatures thanks to layers buildup on electrodes.
In all situations you must consider yourself conditions. For short (30min) night runs, battery could be on your head and unsheltered, because it will keep alowable temperature for some time. For all longer activities or activities with high freeze or wind, its a must to keep the battery under your outter clothes layer or thermally isolate battery, such as using our softshell pouch.
However, if you are in life threatening situation, safe your life rather than battery. One use in cold enviroment will not damage battery much. Severe damage is allways caused by long term low temperature usage.
 Battery University - Battery Testing and Safety, https://batteryuniversity.com/learn/article/battery_testing_and_safety
 Performance and Safety of COTS 18650 Li-ion cells from Various Manufacturers, PDF, NASA, 2013
 Specification of product Samsung INR18650-35E, PDF, Samsung SDI, 2015
 Specification of product Panasonic/Sanyo NCR18650B, PDF, Panasonic/Sanyo
 Specification of product Panasonic/Sanyo NCR18650GA, PDF, Panasonic/Sanyo
 Performance and Safety Testing of Panasonic 2.9Ah Li-ion NCR 18650 Cells, PDF, NASA, 2009