My son was a boy scout and many local troops have monthly camping trips year round. They get a "Zero Hero" patch for sleeping outdoors in below zero weather.

If a bunch of pre-teen and young teenage boys can spend a weekend outdoors in that kind of cold, one can manage on a bike for an hour. It does take the right clothing however and feet can be tough. It helps to keep the rest of your body good and warm. If your core starts getting cold, your body reacts by not circulating as much blood out to the extremities.

For the feet themselves, make sure your toes have plenty of room. Wear wool socks and shoes/boots that will both block the wind and keep cold from getting transmitted up through the soles. There are replacement insoles that can help. Chemical toe warmers help too.

If your feet start getting cold during your ride, stand up and pedal or hop off your bike and stomp your feet for a few minutes. That will help a lot.

I guess I'm not sure how it is for people that live in normal climates but having fingers and toes go numb for short periods of times happens on regular basis during the winter and I don't think of it as dangerous.

For the most part cycling gear isn't designed for very cold weather with some exceptions. However, there are lots of other outdoor winter activities and suitable clothing isn't hard to find.