Yeah, frostbite is a serious condition but occurs at lower temps. At combined temperatures lower than -20C and 20km/h winds frostbite on any exposed skin is ensured in a healthy adult in about 30 minutes. So anytime you're on a bicycle at -20C you are at risk of frostbite on any exposed skin and that is if the wind is dead calm, reduce that time if there is a wind blowing.

There are other complications such as chilblains, which I mentioned. These arise from chronic exposure of skin to lower temperatures though - but can contribute/complicate your proneness of getting frostbite.

Everybody is sensitive to different levels of cold, elderly can get hypothermia at room temperature. So take care!