Praise be to Allah.
It is permissible to prostrate on soft surfaces like blankets etc., so long as the worshipper can place his forehead and nose firmly on the surface when prostrating. What is not allowed is prostrating on something too soft, in which the worshipper’s face will sink and not be firmly placed.
Ibn al-Hamaam said in Fath al-Qadeer (1/304): It is permissible to prostrate on grass, straw and cotton, if it is firmly laid on the ground, and likewise compacted snow, but not if his face will sink into it or it is not firmly laid on the ground. End quote.
Ibn al-Qayyim said in al-Bahr al-Raa’iq (1/337): The basic principle is that just as it is permitted to prostrate on the ground, it is also permitted to prostrate on anything that is like the ground, where his forehead may be firmly placed, meaning that if he presses hard, his head will not sink any further down. End quote.
Based on this, there is nothing wrong with prostrating on an item like a blanket or mattress, if it is firm and will remain stable no matter how much pressure a person puts on it.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about the ruling on prostrating on a sponge pad. He replied: If the sponge is thin and will flatten out when he prostrates, then there is nothing wrong with it.
Fataawa Ibn ‘Uthaymeen (13/184).
And Allaah knows best.