In addition to the problem of having extremely low capacity at very cold temperatures, there is a more severe issue: Charging at very low temperatures can result in elemental lithium being permanently plated onto the anode.
According to Battery University, this occurs on some Li-ion batteries at temperatures as high as 0°C (32°F):
Battery University said:
Many battery users are unaware that consumer-grade lithium-ion batteries cannot be charged below 0°C (32°F). Although the pack appears to be charging normally, plating of metallic lithium can occur on the anode during a subfreezing charge. The plating is permanent and cannot be removed with cycling. Batteries with lithium plating are known to be more vulnerable to failure if exposed to vibration or other stressful conditions. Advanced chargers, such as those made by Cadex, prevent charging Li-ion below freezing.
I seriously doubt the battery in the LEAF would be damaged at that temperature, but there must be a problem below -20°F or they would not have added the heaters.
I wonder if the BMS also prevents charging at those very low temperatures. If so, your only recourse if the battery gets that cold would be to somehow warm it above -20°F (or perhaps higher if there is hysteresis built in) before trying to charge the car again.