Swami Vishwananda talks about Covering the Hair

Sri Swami Vishwananda says "You see the hair is very important. All of the senses of the body are controlled by the hair. The hair normally is cut as the first offering. In the Hindu tradition, the first thing when the baby is born is to shave the hair completely and offer it to Narayana. Also in India there are several pilgrimage places where when you go there you give your hair as an offering, because the hair symbolises everything. It symbolizes the fullness and your humility in front of God, the willingness to accept the Divine Grace and power so that God can guide you and protect you.

Also it is a debt towards the Divine, so you are giving Him something that belongs to you, this physical body. Well, it does not belong to you, this physical body. It was given to you to advance you on your spiritual way but it is closer to you, your identity. The closest thing is not even the clothes but it is a part of yourself, your hair. You offer it to Him.
In Buddhism when they take their vow they always cut the hair, so also in Christianity it is the same. Again there is a similarity, a joining together."