This room has no doors, no windows and no other hole large enough for the prisoner to escape via. He has no tools, he has no assistance. He does have a table and a chair in the centre of the room. The room is quite large, walls are two foot thick.
How can the prisoner escape?
First he rubs his finger on the table until it is sore, cuts the table in half with the saw. Puts the two halves of the table together to make it whole. Climbs in the hole and shouts until he is hoarse. Climbs on the horse and rides away.