While performing obligatory prayers or even , Tahajjud , in the middle of the night, do not pray on your sleeping clothes. Praying in sleeping clothes show one's remissness in prayers. 

Prayers are for Allah. Even when performing Tahajjud alone at night, you are standing to pray for your Creator, Allah. From the beginning to the end, you are in the presence of Allah. So, put on your best attires for praying. 

It is not forbidden to pray in sleeping clothes. As long as they are clean, it is permissible to use them in praying. It must also cover the parts of the body which need to be covered while praying. However, praying in sleeping clothes are considered unethical. Because putting clean and best clothes is in obedience to the command of Allah.

Allah Says in Chapter no. 7 verse no. 31: 

يٰبَنِىۡۤ اٰدَمَ خُذُوۡا زِيۡنَتَكُمۡ عِنۡدَ كُلِّ مَسۡجِدٍ

Meaning: O Children of Adam! Take your adornment (by wearing your clean clothes) while praying [al-A'raaf 7:31].

Therefore, at least put on another piece of clean cloth over your sleeping clothes for prayers.

Putting clean clothes for praying shows your undivided attention and love for the prayers. There is nothing a Muslim should pay more attention, rather than their Salat.