When I lived in Michigan, I would ride to down to 15 degrees. In those days before clipless pedals, I could not wear booties (large feet). Below 15 degrees the wind chill was too much for me to get any work out on a bike so I would switch to cross country skiing. However, in Lansing, temperatures that cold did not persist too long.

I did go out once cross country skiing at 20 below for about 5 hours. I came back in with ice frozen to my cheekbones but no frost bite. If you are active in cold temperatures, it is amazing how the metabolic heat keeps you comfortable.