It possibly could, but you need moisture in the air to cause evaporative cooling, and at those temps, the air is pretty dry.
Evaporative cooling stops when the moisture freezes.
Wind chill refers not to the temperature reached, but rather to how rapidly heat is lost in getting to that temperature.
IOW, a person (or anything else above ambient temperature) outside at 0F and 10 mph wind (-16F windchill) would lose heat as fast as a person at a temperature of -16F and no wind. But once he reached 0F he wouldn’t cool below that temperature no matter how long outside.