All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It wasn`t established in authentic Hadiths that covering the head during prayer or while out of house is Mustahab (Commendable). However, in some countries and communities, skullcaps are worn for adornment, and they still are.
In addition, it was established that the Prophet (PBUH) used to keep his head covered with a turban, and he also used it as ornament.
Therefore, if covering the head is an ornament and a commendable custom in a certain country, then wearing a skull cap or turban when going out, particularly for praying at the mosque, is similarly commendable from the perspective of Sharia. This is since Allah the Almighty Says (What means): "O Children of Adam! wear your beautiful apparel at every time and place of prayer: eat and drink: But waste not by excess, for God loveth not the wasters." {Al-A`raf, 31}.
The ruling of Sharia on this matter depends on people`s different customs and the way they dress. Thus, if the people of a certain country or a certain time regard covering the head for men as an ornament, then it becomes commendable for the latter to do so, or else this matter remains within the circle of the lawful acts since there is no special Hadith commending this Sunnah and promising a special reward for performing it.
As for the Prophet`s (PBUH) wearing the turban and carrying a walking stick, it is an ordinary act that the Arabs used to do, not a legislative act indicating that this is commendable or should be followed by the people.
Al-Shatibi stated: "Customs fall into two types: First: Sharia customs supported by textual evidence from the Quran or the Prophetic Sunnah. Second: Customs for which there is no textual evidence from the Quran or the Prophetic Sunnah supporting or negating them, such as the customs that differ from country to country." [Al-Moafaqaat, vol./pp.489].
Some scholars have mentioned that covering one`s head during prayer is unconditionally commendable. It is stated in a Shafie book: "It is disliked for a Muslim to uncover his head during prayer because the Sunnah is to embellish the prayer with covering the head and the body." [Hashiyat E-anat at-Talibeen, vol./pp.226].
However, the view of Al-Shatibi is more suitable to change in time and place. And Allah the Almighty Knows Best.