The most common problems when temperatures drop below freezing are frostbite and hypothermia. The latter can become very serious very quickly. Hypothermia can lead to heart arrythmias and then to having a heart attack.
Frostbite warning signs include numbness, tingling or pain to the extremities. The nose, hands and feet are most at risk.
To prevent both these conditions you should limit your time outside. And if you do go outside, wear several layers including a hat, gloves, a scarf, a heavy coat and heavy boots.
For people with asthma or any lung condition, you should wear a scarf over your mouth and nose. This will warm the air before it goes to your lungs.
Other things to keep in mind is drinking alcohol can numb your senses. Make sure to limit your intake and stay inside while drinking.
And for everyone, severely cold weather can weaken the immune system, so make sure you to wash your hands frequently and take care of yourself.