When a weather forecast calls for bitterly cold weather it means that the weather will be so cold that it will cause a sharply painful or stinging sensation on your skin in a short amount of time.
Bitterly cold weather can be any temperature below freezing and if the wind is blowing you're gonna be even colder than it feels.
That is also the wind chill factor.
I can stand being outside in below freezing weather for around 1 hour at a time but when the wind starts blowing I cannot stand being outside in the cold wind for longer than 10 minutes.
I kind of like cold weather because there are no bugs and I'm not sweating but when the wind blows then I hate it.
The bitterly cold weather can also mean dangerously cold weather.