Can You Pray with Your Shoulders Exposed?
Question

Does a man have to cover his shoulders whilst praying? Is praying with bare shoulders permissible or prohibited?
Praise be to Allah.Is it obligatory to cover the `Awrah in prayer?
The jurists unanimously agreed that it is obligatory to cover the `Awrah whilst praying . The man’s `Awrah is between the navel and the knee, and some of them include the navel and the knee in the `Awrah. 
Is covering the shoulders in prayer obligatory?
They differed as to whether it is obligatory to cover the shoulder, which is the area between the shoulder blade and the neck. The majority are of the view that it is not obligatory , but the Hanbalis are of the view that it is mandatory in obligatory prayers in particular, and that the prayer is not valid otherwise. 
The majority quoted as evidence the Hadith narrated by Al-Bukhari (361) and Muslim (3010) from Sa`id ibn Al-Harith who said: We asked Jabir ibn `Abdullah about praying in a single garment and he said: I went out with the Prophet (peace and blessings of Allah be upon him) on one of his journeys and I came at night for some purpose, and I found him praying and I was wearing a single garment. I wrapped myself in it and prayed beside him. When he had finished he said: “What is this walking at night O Jabir?” I told him of my need, and when I had finished he said: “What is this wrapping that I see?” I said: It is too small. He said: “If it is large enough, wrap it around the body, and if it is too small, tie it around your waist.” 
When he asked him about walking at night, he was asking him why he had come at this time. 
The Hanbalis quoted as evidence the Hadith narrated by Al-Bukhari (359) and Muslim (516) from Abu Hurayrah (may Allah be pleased with him) who said: The Prophet (peace and blessings of Allah be upon him) said: “No one of you should pray in a single garment with nothing on his shoulders.”
The majority of scholars interpreted this as meaning it is recommended, so as to reconcile between the reports. 
An-Nawawi (may Allah have mercy on him) said in Sharh Muslim: With regard to the words of the Prophet (peace and blessings of Allah be upon him), “No one of you should pray in a single garment with nothing on his shoulders”, the scholars said: The reason behind it is that if he wraps it around his waist and no part of it is on his shoulders, there is no guarantee that his `Awrah will not become uncovered , unlike if he places part of it over his shoulder. And because he may need to hold it with his hand or both hands so he will be distracted by that, and will miss out on the Sunnah of placing the right hand over the left hand beneath his chest, and raising the hands when it is Sunnah to do so, and so on. And because he is not covering the upper body which is the place of adornment. Allah says (interpretation of the meaning): {Take your adornment (by wearing your clean clothes)} [Al-A`raf 7:31].
Moreover Malik, Abu Hanifah, and Ash-Shafi`i (may Allah have mercy on them) and the majority of scholars said that this is a prohibition in the sense of being disliked, and it is not prohibited. So if a man prays in a single garment that covers his `Awrah, but no part of it is on his shoulder, then his prayer is valid although it is makrooh, whether he was able to put something on his shoulder or not. 
Ahmad and some of the Salaf (may Allah have mercy on them) said: If he was able to put something over his shoulder, his prayer is not valid unless he covers his shoulder, because of the apparent meaning of the Hadith. And another report was narrated from Ahmad (may Allah have mercy on him) stating that his prayer is valid, but he is sinning by not doing that. 
The evidence of the majority is the words of the Prophet (peace and blessings of Allah be upon him) in the Hadith of Jabir (may Allah be pleased with him): “If it is big enough, wrap it around the body, and if it is too small, tie it around your waist.” This was narrated by Al-Bukhari, and by Muslim at the end of the book in his lengthy Hadith. (End quote)
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said, in the commentary on Sharh Zad Al-Mustaqni`: Differentiating between obligatory and optional prayers is contrary to the apparent meaning of the Hadith. Moreover, the author said: “with one of his shoulders” but the Hadith indicates that both shoulders must be covered. What the author said is the well-known view of the Madhhab. 
The second opinion is that covering the shoulders is Sunnah and not obligatory, and there is no difference between obligatory and optional prayers, because of the Hadith, “if it is too small, tie it around your waist”. This view is the more correct one, and it is the view of the majority. The idea that there should be something on the shoulders is not because the shoulders are `Awrah , rather it is so that the clothing may be complete and the waist wrapper be tied properly, because if it is not secured at the shoulders, it may come loose and fall. In this case the covering of the shoulders is sought for another purpose; it is not sought in and of itself. (End quote from Ash-Sharh Al-Mumti`, 2/168). 
Also please see Al-Mughni (1/338) and Al-Majmu` (3/180) 
To sum up, it is not obligatory for a man to cover his shoulders or shoulder blades when praying, but it is recommended to do so as an adornment and out of respect for the prayer and the fact that he is standing before his Lord, may He be Glorified and Exalted; but if he prays with his shoulders or shoulder blade bare, his prayer is valid. 
And Allah knows best.