Every part of the human body has been placed respectively to serve its purpose. Some parts, organs and limbs play an important and vital role whilst others have a minor supporting role. At the outset, looking at the external human appearance its beauty is manifest immediately and, it's at this juncture that we are most grateful to Allah Ta'ala.
Consequently, we are not owners of ourselves i.e. we have been entrusted by Allah Ta'ala with our physical body and internal self. Therefore, as this is a Trust (Amaanat), it does not belong to us; and as a result, we have to obey and respect its obligations. If the Maker requires us to fulfil a certain requirement then we must fulfil it.
A woman is required to keep and wear her hair without cutting it short.
Allah Ta'ala has concentrated the physical beauty of the human being in the upper part of the body, i.e. the face. The face is probably the most important feature in the whole external anatomy of the human being. In fact, every effect and reaction becomes evident on the face instantly. Hence, the face is the central part of the whole body exposed entirely and at all times.
It is obvious that, what surrounds the face displays an important value and forms a protective gear. Moreover, it displays the beauty and identity of a person. Therefore, the long hair of the woman professes her beauty, the one most powerful image of a female.