Can Women Wear Kohl When They Go out?
Question

Why is it not permissible to wear kohl when going out of the house?
Praise be to Allah.Should women cover their beauty and adornment before non-Mahram men?
Every believing woman is obliged to cover her beauty and adornment before non-Mahram men, because Allah says (interpretation of the meaning): 
“And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way, or outer palms of hands or one eye or dress like veil, gloves, headcover, apron), and to draw their veils all over Juyoobihinna (i.e. their bodies, faces, necks and bosoms) and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of feminine sex. And let them not stamp their feet so as to reveal what they hide of their adornment. And all of you beg Allah to forgive you all, O believers, that you may be successful” [An-Nur 24:31]
Adornment includes kohl , makeup, jewellery, etc. 
With regard to the words at the beginning of the verse – “And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent” – what is meant by “that which is apparent” is the clothing, `Abayah (outer garment) and headcover, and whatever appears unintentionally, because of the wind, for example. 
Ibn Kathir (may Allah have mercy on him) said:
“This means she should not show anything of her adornment to non-Mahrams, apart from that which cannot be hidden. Ibn Mas`ud said: Such as the Rida ‘ (cloak) and clothes, i.e., what the Arab women used to wear of a Miqna` (a kind of outer garment) and what appears below from the garment. There is no sin in that, because this is something that cannot be hidden. That is like what appears of a woman’s lower garment, and what cannot be hidden.” (Tafsir Ibn Kathir, 3/274) 
Is covering the face obligatory?
Some of the scholars interpreted the external adornment as referring to the face and hands, but that is a less correct view, because there is a great deal of evidence that shows that it is obligatory for a woman to cover her face .
The scholar Muhammad Al-Amin Ash-Shanqiti (may Allah have mercy on him) said:
“The more correct of the two views in my opinion is the view of Ibn Mas`ud (may Allah be pleased with him), that the external adornment is that which when one looks at it, one cannot see any part of the woman’s body. We say that this view is more correct because it is the most cautious view, and is farthest removed from causes of Fitnah (temptation), and is purest for the hearts of men and women. It is obvious that a woman’s face is the focus of her beauty, and seeing it is one of the greatest means of temptation. As is well known in Shari`ah, this is the best means of avoiding falling into something prohibited.” (Adwa’ Al-Bayan, 6/200) 
The basic principle is that a woman should cover her entire face, but it is permissible for her to uncover her eyes so that she may see, subject to the condition that showing her eyes will not lead to any Fitnah due to her wearing kohl or having wide openings in her Niqab (face cover). 
The evidence for this concession in wearing Niqab and uncovering the eyes is the report narrated by Al-Bukhari (1838) from `Abdullah ibn `Umar (may Allah be pleased with him), according to which the Prophet (peace and blessings of Allah be upon him) said: “A woman in Ihram should not wear Niqab or wear gloves.” This indicates that it is permissible for women who are not in Ihram for Hajj or `Umrah to wear niqab . 
Abu `Ubayd said, describing the Niqab that was worn by the Arabs: “It is that which shows the eye-socket; they used to call it al-waswasah and al-burqa’.” (Fatawa Al-Lajnah Ad-Da’imah, 17/171) 
Why shouldn’t women show their adornment?
The reason why it is prohibited to show this adornment is so as to protect women’s chastity and honour, and to close the door to temptation and prevent her being tempted or tempting others. Those who are sick at heart may have hopes concerning those who show their adornment, but they will leave the one who is modest and covered alone. 
Islam closes the doors that lead to men being tempted by women and vice versa. Islam enjoins lowering the gaze and forbids wanton display, free mixing and being alone with women. Women are warned against going out wearing perfume or travelling without a Mahram. This is reflective of the perfection of Islam, for men by nature are affected by women, and if this is not prevented then there will be much Fitnah (temptation and tribulation), and corruption will become widespread, as we can see in societies that have neglected the guidelines and rulings of the Shari`ah. 
Can women wear kohl when they go out?
It says in Fatawa Al-Lajnah Ad-Da’imah (17/128): Many women in Egypt put kohl on their eyes, and if I tell them that wearing it for adornment is prohibited, they say that it is Sunnah. Is that true? 
Answer:
“Using kohl is prescribed in Islam , but it is not permissible for a woman to show any of her adornment, whether that is kohl or anything else, to anyone other than her husband or Mahrams. Allah says (interpretation of the meaning): “and not to reveal their adornment except to their husbands…” 
In conclusion, it is not permissible for a woman to wear kohl in front of non-Mahram men, because it comes under the heading of adornment which she is required to conceal. If she is going from one house to another, where no non-Mahram will see her, then there is nothing wrong with her wearing kohl in that case. 
And Allah knows best.