Firstly: 

It is not permissible to uncover the face of the deceased when he is placed in the lahd (niche in the grave), whether the deceased is a man or a woman. For more information please see the answer to question no. 48959 

Secondly: 

With regard to covering the deceased, many of the scholars (may Allah have mercy on them) regarded it as mustahabb to cover the bier of a woman. That was narrated from some of the Sahaabah (may Allah be pleased with them). 

An-Nawawi (may Allah have mercy on him) said: It is mustahabb to use a na‘sh for a woman. The na‘sh is a frame that is placed over the woman on the bier, and is covered with a cloth so as to screen her from people’s eyes. … They quoted as evidence for that the story of the funeral of Zaynab the Mother of the Believers (may Allah be pleased with her). It was said that she was the first Muslim woman to be carried on a bier covered with a na‘sh. Al-Bayhaqi (may Allah have mercy on him) narrated that Faatimah, the daughter of the Messenger of Allah (blessings and peace of Allah be upon him, and may Allah be pleased with her), left instructions that this should be done for her, and they did that. If this report is saheeh, she died many years before Zaynab. As for the report narrated by al-Bandaneeji, that the first time this was done was in the funeral of Zaynab the daughter of the Messenger of Allah (blessings and peace of Allah be upon him), and that the Messenger of Allah (blessings and peace of Allah be upon him) ordered that that be done, this is untrue and is not known; I draw attention to it so that no one will be deceived by it.

End quote from Sharh al-Muhadhdhab, 5/234 

In Haashiyat ad-Dasooqi (1/418) it says: It is recommended to conceal the dead woman with a frame to be placed on top of the bier, because it is more effective in covering. End quote. 

Ibn Qudaamah (may Allah have mercy on him) said: It is mustahabb to place over the bier of a woman something made of wood or palm branches, like a frame, over which a cloth should be placed, to be more covering for her.

End quote from al-Mughni, 2/211 

Al-Bahooti (may Allah have mercy on him) said: It is mustahabb to cover the bier of a woman with a frame.

End quote from Daqaa’iq Ooli’n-Nuha, 1/369 

The texts of the scholars which speak of it being mustahabb to cover the bier of a woman with a frame indicate that a man should not be covered, rather he may be left uncovered (i.e., with no frame over his bier).

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Should a makabbah be placed over the bier or not? 

The makabbah is like a frame made of bent sticks that is placed over the bier, and a cloth is placed over it. 

Answer: if the deceased is female, then yes. Many of the scholars regarded it as mustahabb because that is more covering for her. 

Al-Bayhaqi (may Allah have mercy on him) narrated that Faatimah, the daughter of Muhammad (blessings and peace of Allah be upon him), left instructions that that should be done for her. 

This is done in the Hijaz, but in Najd it is not known, however if someone does it, he is doing something good and should not be denounced for it, because sometimes there are funerals of women in which one may see things that one does not want to see, but if they put this makabbah over her, that would cover her. 

It says in ar-Rawd: If the deceased is a woman, it is mustahabb to cover her bier with a makabbah, because that is more covering for her, and it was narrated that this was done for Faatimah on her instructions. And a cloth should be placed over the makabbah. The same applies if the deceased was a hunchback or the like, so as to conceal this deformity. 

In the case of a man, it is not Sunnah to do this; rather he should be left as he is, because there is a benefit in that, which is the powerful lesson to be learned by those who were with him yesterday and see him now, a dead body on this bier. But if he is covered with an abayah, as is done in our country, there is nothing wrong with that.

End quote from ash-Sharh al-Mumti‘, 5/356 

And Allah knows best.