What is the process of the release of the horse in the Ashvamedha Yagna?

 

The process of the release of the horse in the Ashvamedha Yagna, a ritual performed by ancient Indian kings to establish imperial sovereignty, is primarily detailed in the Shukla Yajurveda and the Shatapatha Brahmana (specifically in the thirteenth Kanda).

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However, the term Aśvamedha, which was first used in Rig Veda, had been coined by the rishis indicating purifying human consciousness of a spiritual practitioner and consequential attainment of SELF-REALISATION or BLISS or Immortality.

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The release of horse was also mentioned in the Rig Veda 3.53.11 but it was used in esoteric sense, indicating journey of the INDIVIDUAL SOUL (aśva - अश्व ) conquering one’s own weaknesses/illusions (in all directions and conquering enemies therein).

उप प्रेत कुशिकाश्चेतयध्वमश्वं राये प्र मुञ्चता सुदासः । राजा वृत्रं जङ्घनत्प्रागपागुदगथा यजाते वर आ पृथिव्याः ॥
upa preta kuśikāś cetayadhvam aśvaṃ rāye pra muñcatā sudāsaḥ | rājā vṛtraṃ jaṅghanat prāg apāg udag athā yajāte vara ā pṛthivyāḥ ||

English translation:

Come forth, Kuśikas; make yourselves known. Release the horse of Sudās, to (gain) wealth. The king will smash the obstacle to the east, to the west, to the north. Then he will sacrifice on the best part of the earth.

 

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Please note that the rishi had mentioned about conquering of only 3 directions, ie., East, West and the North.

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If understood in esoteric sense, it indicates conquering of 3 weaknesses or getting released from the three (3) bonds/fetters - pāśān of King Varuṇa.