The cold wind penetrates one's bones.

Both expressions are correct.

"Bitter wind" and "bitter wind" are both words used to describe the cold weather. Their meanings are basically the same, but their expressions are different. The word "biting cold wind" comes from Wang Changling's "Xia Sai Qu" in the Tang Dynasty: "Drink horses when we cross the autumn waters! The stream is as cold as the wind and as sword, which means the cold wind is as cold as bone.

And "biting cold wind" is also a word to describe the cold weather. It means the wind is biting.

Generally speaking, "biting cold wind" and "biting cold wind" are words used to describe extremely cold weather, but their expressions are slightly different. Bitter wind focuses more on the feeling that the cold wind penetrates into the bone marrow, while bitter wind focuses more on the fierceness and coldness of the cold wind.