That translation on wikipedia is of Griffith and other colonial British translators and is completely wrong. Basically there is one verse from Shatapatha Brahmana and four verses from Yajur Veda which has been completely mis translated and all the vulgar translations on any website or book is from these 5 verses only.
I will present the original translation to all these verses with citations from 7 different scholars in English and Hindi below.
1) "अश्वस्य शिश्न महिष्युपस्थे निधते " (Satapatha Brahmana-13/5/2/2)- Prayer by Sage Yagyavalkya.
Meanings: 1) अश्वस्य- King who is performing the yajña (" क्षत्र वा अश्व: क्षत्र राजन्य: | " Shataptha Brahmana-13/4/1/12);
2) शिश्न- One with opulence (" शिश्नमिन्द्र "- Shataptha Brahmana-12/9/2/2 अर्थात इंद्र शिश्न है |);
3) महिषी- Speech (" महिषी वा वाक् "-शतपथ 6/5/3/4, For speech is a mahishi);
4) उपस्थये- Lap; निधते- kept or made seated;
Translation: May the King's might and brilliance be expressed in his speech. (May the voice of the King roar like a lion to maintain law and order in the state and to protect his citizens and all others who approach him for shelter. For it is the duty of the King to prevent any adharmik activity from happening in the kingdom.)
2) "प्रा॒णाय॒ स्वाहा॑पा॒नाय॒ स्वाहा॑ व्या॒नाय॒ स्वाहा॑। अम्बे॒ऽअम्बि॒केऽम्बा॑लिके॒ न मा॑ नयति॒ कश्च॒न। सस॑स्त्यश्व॒कः सुभ॑द्रिकां काम्पीलवा॒सिनी॑म्॥१८॥" ~ Yajur Veda-23.18
Translation - We should accept the words of knowledge, the exponent of Prana, Apana and Vyana (Vital life airs in our body). On receiving these knowledge, no temptation of the world can defeat us. A person who engages in actions in this (material) world according to the right knowledge of Vedic Scriptures(Gyana Cakshu) lives comfortably attaining the welfare(blessings) of Lakshmi.
3) "ग॒णानां॑ त्वा ग॒णप॑तिꣳहवामहे प्रि॒याणां॑ त्वा प्रि॒यप॑तिꣳहवामहे निधी॒नां त्वा॑ निधि॒पति॑ꣳ हवामहे वसो मम। आहम॑जानि गर्भ॒धमा त्वम॑जासि गर्भ॒धम्॥१९॥" ~ Yajur Veda-23.19
Translation - Worshiper of The Supreme Lord(Gana Pati) master of all the ganas, 33 Million Demigods. Let me know you as my ultimate shelter. Let me walk towards you who conceives the whole world. You are the one who activates and controls the material nature(prakriti) which gives birth to (manifests) this material universe. Please give me the ultimate destination which is the shelter at your Lotus Feet.
4) "ताऽउ॒भौ च॒तुरः॑ प॒दः स॒म्प्रसा॑रयाव स्व॒र्गे लो॒के प्रोर्णु॑वाथां॒ वृषा॑ वा॒जी रे॑तो॒धा रेतो॑ दधातु॥२०॥" ~Yajur Veda-23.20
Translation - The King and his subjects in unison, magnify the four stages of Dharma, Artha, Kama, Moksha where with they reside happily in their country. The King, the chastiser of the wicked, full of knowledge, the possessor of strength and prowess, lends valour to his subjects.
5) "उत्स॑क्थ्या॒ऽअव॑ गु॒दं धे॑हि॒ सम॒ञ्जिं चा॑रया वृषन्। य स्त्री॒णां जी॑व॒भोज॑नः॥२१॥" ~Vajur Veda-23.21
Translation - To stop adultery and crime against women in the nation, the King should hang the wrongdoer man(aggressor) upside down and let the knowledge of the disadvantages of adultery and the benefits of abstinence to be propagated in the nation, so that the hearts of the people can be transformed.
For word by word meaning of the above verses you can checkout-
https://www.scribd.com/doc/147822000/Yajur-Veda-Chapter-23
For more English and Hindi translations to these verses you can checkout-
- https://vedicscriptures.in/yajurveda/23/19
- https://vedicheritage.gov.in/flipbook/Shukla_Yajurveda_madhyandina_Subodh_Bhasya/#book/398
- https://www.google.co.in/books/edition/Yajurveda/drT4K1GXbnsC?hl=en&gbpv=1&dq=yajur+veda&printsec=frontcover
Basically what happens is that- The queens circumambulate the dead horse(after it is slained) reciting mantras and make three symbolic marks on the body of the horse using a golden needle. Then the chief queen along with other royal ladies and their maidservants sits near the slained horse at a distance(i.e near the yagya kund of Vishnu where the horse will be sacrificed), offering ahuti to the fire(yajña) as it can be seen from ~Yajur veda-23.18 and praying for the welfare and prosperity of the King who is performing this yajña and his kingdom(including the whole world and people in general). After this the horse is finally sacrificed to Vishnu and simultaneously given a heavenly body. As it can been seen in the Mahabharata and Ramayana. https://www.sacred-texts.com/hin/m14/m14089.htm
One more thing to notice is that where ever the description of Ashwamedha Yagya is given in the scriptures the sanskrit word used is either "sits or resided near the dead horse" but it has been mis translated into "sleeping with the dead horse".
If you liked it you can share these correct translations with anyone who needs it.