The khadag comes in several colours and Mongolian practice reaches for blue far more often than for any other. The reason given is direct: the sky is blue, the sky is tenger, and tenger is what the steppe traditions address before anything else. White, yellow, green and red khadag all exist and carry their own associations, and in monastic contexts white predominates as it does in Tibet, but blue is the everyday Mongolian answer.
Its uses run across every register of life. A khadag is laid on an ovoo, the stone cairn built at a pass or a summit. It is tied to a tree at a spring. It is draped over an image in a temple, wrapped around the shaft of a sulde, and knotted to the frame of a vehicle. It is presented to a guest, held out across both open palms with a slight bow, and it goes with a marriage, a birth, a departure and a death.
That range is the point. The khadag is not a specialised ritual instrument that a specialist handles. It is a piece of cloth that anybody can carry and give, and its meaning is supplied almost entirely by the act of offering rather than by anything intrinsic to the object.
Nothing about the cloth itself is consecrated in advance. A khadag bought in a shop that morning is a khadag; it becomes an offering at the moment it is laid down or handed over, and not before.