Can a Man See a Woman before Marriage?
Question

I read the hadiths about the prophet peace be upon him allowing the man to see the woman before deciding whether to marry her or not. My question is, what exactly is the person allowed to see exactly? Is he allowed to see her hair (entire head)?
Praise be to Allah.Importance of lowering the gaze in Islam
Islam commands us to lower our gaze and forbids looking at non-Mahram women. This is in order to purify people’s souls and protect their honour.
Necessity of seeing one’s fiancée
There are, however, certain exceptions in which it is permissible to look at a non-Mahram woman for reasons of necessity, one of which is in the case of proposing marriage, because it is the basis on which a very important decision affecting a person’s life will be taken.
Hadiths supporting looking at one’s fiancée
There are texts which indicate that it is permissible to look at one’s fiancée, as follows:

From Jabir ibn `Abdullah (may Allah be pleased with him): “The Messenger of Allah (peace and blessings of Allah be upon him) said: `If one of you proposes marriage to a woman, if he can look at her to see that which will encourage him to go ahead and marry her, then let him do so.’ I proposed marriage to a young woman, and I used to hide where I could see her, until I saw that which encouraged me to go ahead and marry her, so I did so.’” According to another report he said, `a young woman of Bani Salamah. I used to hide from her, until I saw that which encouraged me to go ahead and marry her, so I did so.” (Narrated by Abu Dawud; Sahih Abu Dawud, 1832, 1834)
From Abu Hurayrah (may Allah be pleased with him): “I was with the Prophet (peace and blessings of Allah be upon him) when a man came and told him that he had married a woman of the Ansar. The Messenger of Allah (peace and blessings of Allah be upon him) said to him, ‘Have you seen her?’ He said, “No.” He said, “Go and look at her, for there is something in the eyes of the Ansar.” (Narrated by Muslim, 1424 and by Ad-Daraqutni, 3/253 (34))
From Al-Mughirah ibn Shu`bah (may Allah be pleased with him): “I proposed marriage to a woman, and the Messenger of Allah (peace and blessings of Allah be upon him) said: ‘Have you seen her?’ I said, ‘No.’ He said, ‘Look at her, because it is more fitting that love and compatibility be established between you.’” According to another report: “So he did that, and he married her and mentioned that they got along.” (Narrated by Ad-Daraqutni, 3/252 (31, 32) and Ibn Majah, 1/574)
From Sahl ibn Sa`d (may Allah be pleased with him): “A woman came to the Messenger of Allah (peace and blessings of Allah be upon him) and said: “O Messenger of Allah, I have come to give myself to you (in marriage).” The Messenger of Allah (peace and blessings of Allah be upon him) looked at her closely, then he lowered his head. When the woman saw that he had not made a decision about her, she sat down. One of his Companions stood up and said, O Messenger of Allah, if you do not want her, then marry her to me…’” (Narrated by Al-Bukhari, 7/19; Muslim, 4/143; An-Nisa’i, 6/113 with the explanation of As-Suyuti and by Al-Bayhaqi, 7/84)

The sayings of the scholars on the extent to which one may look at one’s fiancée
Ash-Shafi`i (may Allah have mercy on him) said: “If he wants to marry a woman, he is not allowed to see her without a headcover. He may look at her face and hands when she is covered, with or without her permission. Allah says (interpretation of the meaning): {… and not to show off their adornment except only that which is apparent…} [An-Nur 24:31]. He said: `The face and hands.’” (End quote from Al-Hawi Al-Kabir, 9/34).
Imam An-Nawawi (may Allah have mercy on him) said in Rawdat At-Talibin wa `Umdat Al-Muftin (7, 19-20): “When (a man) wants to marry (a woman), it is preferable for him to look at her so that he will have no regrets. According to another view, it is not preferable but it is allowed. The first view is correct because of the Hadiths, and it is permitted to look repeatedly, with or without her permission. If it is not easy to look at her, he may send a woman to check her out and describe her to him. A woman may also look at a man if she wants to marry him, for she will like in him what he likes in her. What is permissible for him to look at is the face and hands, front and back. He should not look at anything else.”
Abu Hanifah permitted looking at the feet as well as the face and hands. (End quote from Bidayah Al-Mujtahid wa Nihayyat Al-Muqtasid, 3/10)
“It is permissible to look at the face, hands and feet, and no more than that.” Ibn Rushd also quoted it as above.
Among the reports from the Madhhab of Imam Malik:

He may look at the face and hands only.
He may look at the face, hands and forearms only.

A number of reports were narrated from Imam Ahmad (may Allah have mercy on him), one of which says that he may look at the face and forearms. The second says that he may look at what usually appears such as the neck, calves and so on.
This was quoted by Ibn Qudamah in Al-Mughni (7/454), Imam Ibn Al-Qayyim Al-Jawziyyah in Tahdhib As-Sunan (3/25-26), and Al-Hafidh Ibn Hajar in Fat-h Al-Bari (11/78)… The reliable opinion in the books of the Hanbalis is the second opinion.
From the above, it is clear that the majority of scholars say that a man is allowed to look at his fiancée’s face and hands, because the face indicates beauty or ugliness, and the hands indicate the slimness or plumpness (literally, `fertility’) of the body.
Abu Al-Faraj Al-Maqdisi (may Allah have mercy on him) said: “There is no dispute among the scholars that he is permitted to look at the face.. the focus of beauty and the place at which one looks.”
Ruling on touching one’s fiancée or being alone with her
Az-Zayla`i (may Allah have mercy on him) said: “It is not permissible for him to touch her face or hands – even if is sure that this will not provoke desire – because she is still prohibited for him, and there is no need for him to do so.” In Durar Al-Bihar it says: “It is not permitted for the judge, the witnesses or the fiancé to touch her, even if they are sure that this will not provoke desire, because there is no need for that…” (End quote from Radd Al-Muhtar `ala Ad-Durr Al-Mukhtar, 5/237)
Ibn Qudamah (may Allah have mercy on him) said: “It is not permitted for him to be alone with her, because she is forbidden and Islam only allows him to look, thus Khulwah (being alone with her) remains forbidden, and because there is no certainty that nothing forbidden will take place if he is alone with her, as the Prophet (peace and blessings of Allah be upon him) said: `No man is alone with a woman, but the devil is the third one present.’ He should not look at her in a lustful or suspicious manner. Ahmad said, in a report narrated by Salih, `He may look at the face, but not in a lustful manner.’ He may look repeatedly, and examine her beauty, because the aim cannot be achieved in any other way.”
The fiancée’s permission to look
A man is permitted to look at the woman to whom he wishes to propose marriage, even without her permission or knowledge. This is what is indicated by the authentic Hadiths.
Al-Hafidh Ibn Hajar (may Allah have mercy on him) said in Fat-h Al-Bari (9/157): “The majority of scholars said: he is permitted to look at her if he wishes without her permission.”
The Hadith scholar Shaykh Muhammad Nasir Ad-Din Al-Albani (may Allah have mercy on him) said in As-Silsilah As-Sahihah (1/156), supporting this view: “Similar evidence is seen in the words of the Prophet (peace and blessings of Allah be upon him) in the hadith, `Even if she does not know.’ This is supported by the actions of the Companions (may Allah be pleased with them), in accordance with the Sunnah, such as Muhammad ibn Muslimah and Jabir ibn `Abdullah, both of whom hid so as to see of their fiancées that which would encourage them to go ahead and marry them…”
Shaykh Al-Albani (may Allah have mercy on him) also said (op.cit., p. 156):
“From Anas ibn Malik (may Allah be pleased with him)” `The Prophet (peace and blessings of Allah be upon him) wanted to marry a woman, so he sent another woman to look at her and said, “Smell her mouth (front teeth) and look at the back of her ankles.” (Narrated by Al-Hakim, 2/166, who said it is authentic  according to the conditions of Muslim, and Adh-Dhahabi agreed with him. Also narrated by Al-Bayhaqi, 7/87. In Majma` Az-Zawa’id (4/507) he said, ‘Narrated by Ahmad and Al-Bazzar, and the men of Al-Bazzar are trustworthy.’)
In Mughni Al-Muhtaj (2/128) it says: “What we understand from this report is that the one who is sent may describe to the one who sends her more than that which he himself may see, so this sending achieves more than just looking.”
For more details, please see the following answers: 93450, 13704, 88130, and 1774.
And Allah knows best.