Aswamedha yajna was a royal rite. It was done only by the Kings to spread their glory throughout the world and for the benefit of their kingdom (rāṣṭram vā aśvamedhaḥ). Regarding its origin and usage of horses the Brihadaranyaka Upanishad says:

सोऽकामयत: मेध्यं म इदं स्याद् , आत्मन्व्यनेन स्यामिति ततोऽश्वः समभवद् यदश्वत् , तन्मेध्यमभूदिति तदेवाश्वमेधस्याश्वमेधत्वम् [Brh. Up. - 1.2.7]

Meaning
He (the first purusha or Brahman) desired "let this (his body) be fit for sacrifice(medha) and let me be embodied by it". Then he became a horse as it swelled. He thought, it has become fit for sacrifice. Hence, the horse sacrifice is called as Aswamedha.




Every successful king had to do these ritual to establish kingdom limits & enhance glory


Here a cut-down small ceremony performed by present day royals still trying to get a feel for their ancestors.



This video shows the Ashwa Poojan Ceremony as done by Prince Lakshyaraj Singh Mewar at The City Palace in Udaipur on 3rd October, 2014. The Ashwa Poojan ceremony is held to show gratitude and to honor the nobility of the horses. According to Hindu mythology, horses are a symbol of loyalty and power. This ceremony included a procession on horse carriages followed by a pooja performed in front of a ceremonial horse. This was followed by an elaborate dinner with the royal family and esteemed guests.