As per (Bala Kanda 1.14.33-35), Devi Kaushalya killed the horse and had sex with him. Is this true?
Sometimes, English translations may be gross/misleading. Here is a transltion from Hindi version of Valmiki Ramayana:
उस समय उन यूपों में तीन सौ पशु बँधे हुए थे तथा राजा दशरथका वह उत्तम अश्वरन्त भी वहीं बाँधा गया था ॥ ३२ ॥
At that time three hundred animals were tied in those sacrificial altars, and the best horse of King Dasaratha was also tied there. 32 ॥
रानी कौसल्याने वहाँ प्रोक्षण आदिके द्वारा सब ओरसे उस अश्वका संस्कार करके बड़ी प्रसन्नताके साथ तीन तलवारोंसे उसका स्पर्श किया ॥ ३३ ॥
Queen Kausalya there performed the rituals of sprinkling the horse from all sides and touched it with three swords with great joy. 33 ॥
तदनन्तर कौसल्या देवीने सुस्थिर चित्तसे धर्मपालनकी इच्छा रखकर उस अश्वके निकट एक रात निवास किया ॥ ३४ ॥
Thereafter, with a steady mind, desiring to observe religious principles, goddess Kausalya stayed
nearthe horse for one night. 34 ॥
तत्पश्चात् होता, अध्वर्यु और उद्गाताने राजाकी (क्षत्रियजातीय) महिषी 'कौसल्या', (वैश्यजातीय स्त्री) 'वावाता' तथा (शूद्रजातीय स्त्री) परिवृत्ति' – इन सबके हाथसे उस अश्वका स्पर्श कराया ॥ ३५ ॥
After that, the Hota, the Adhvaryu and the Udgata touched the horse with the hands of the king’s (Kshatriya) queen Kausalya, (Vaishya woman) Vavata and (Shudra woman) Parivrtti. 35 ॥
As highlighted in above verses, devi Kausalya only had touched the horse with the swords and not really killed it. Also she stayed whole night near the horse, there was no sex involved.
Yes, Kaushalya did kill the horse and then she spent one night with that horse. Killing the horse is part of the Asvamedha sacrifice. It could be possible that Kaushalya killed the horse symbolically by touching the horse three times with the sword; someone else did the real killing. But the horse has to be killed in that sacrifice, there is no doubt about it.
And, she did a sexual act with the dead horse as it is part of the ritual. In Valmiki Ramayana, it is clearly mentioned that the sacrifice was performed according to the Kalpasutra and Brahmana. The Asvamedha sacrifice is described in Yajurveda. White Yajurveda Samhita (Vajasaneyi Samhita) 23.18-32 mentioned the Mantras of Asvamedha sacrifice. The procedure is described in the associated Brahmana known as Satapatha Brahmana (Madhyandin branch). The thirteenth Kanda of Satapatha Brahmana (Madhyandina branch) explains the Asvamedha sacrifice.
Traditional commentator of Shukla Yajurveda Mahidhara explained these verses (Shukla Yajur Veda Samhita 23.18-32) that clearly suggest sexual intercourse between the chief queen (Mahishi) and the dead horse. Bengali translation and commentary on Shukla Yajurveda done by Durgadas Lahiri also very clearly explained these verses which only suggest sexual intercourse with the dead horse. Satapatha Brahmana mentioned clearly that Yajurved Samhita 23.18-32 verses have to be said during the ritual while the chief queen does the sexual act. King's Mahishi (the chief queen who belongs to the Kshatriya cast) has to insert the dead horse's penis inside her vagina. One may find it obscene, but that's what it is. You have to remember that the Asvamedha sacrifice has a connection with ancient fertility rites. This is done for the Kingdom's prosperity. So the chief queen's sexual act with the dead horse signifies that.
Here are the relevant quotes from the Ramayana and the Satapatha Brahmana.
And to these Yupas were bound three hundred beasts, as well as the foremost of the best horses belonging to king Daçarātha. Then Kaucalyā, having performed the preliminary rites, with three strokes slew that horse, experiencing great glee. And with the view of reaping merit Kaucalyā, with an undisturbed heart passed one night with that horse furnished with wings. And the Hotâs and Adhwaryus, and the Uâgatas joined the king's Vâvâtâ along with his Mahishi and Parivriti And priests of subdued senses, well-up in sacrificial rites, began to offer oblations with the fat of the winged-horse, according to the ordinance. And that lord of men, desirous of removing his sins, at the proper time smelt the odour of the smoke arising from the fat, agreeably to the scriptures. And then sixteen sacrificial priests in the prescribed form offered the various parts of the horse unto the fire. It is customary in other sacrifices to offer the oblations by means of a Plaksha bough; but in the horse-sacrifice a cane is used instead. The horse-sacrifice, according to the Kalpa Sutras and the Brāhmanas, extend over three days - Valmiki Ramayana 1.14.32-40
- Now the gods, when going upwards, did not know (the way to) the heavenly world, but the horse knew it: when they go upwards with the horse, it is in order to know (the way to) the heavenly world. 'A cloth, an upper cloth, and gold,' this is what they spread out for the horse: thereon they quiet (slay) it, as (is done) for no other victim; and thus they separate it from the other victims.
- When they quiet a victim they kill it. Whilst it is being quieted, he (the Adhvaryu) offers (three) oblations, with (Vāj. S. XXIII, 18), 'To the breath hail! to the off-breathing hail! to the through-breathing hail!' he thereby lays the vital airs into it, and thus offering is made by him with this victim as a living one.
- With, 'Ambā! Ambikā! Ambālikā! there is no one to lead me,'--he leads up the (four) wives: he thereby has called upon them (to come), and, indeed, also renders them sacrificially pure.
- With (Vāj. S. XXIII, 19), 'We call upon thee, the host-leader of (divine) hosts, O my true lord!' the wives walk round (the horse), and thus make amends to it for that (slaughtering): even thereby they (already) make amends to it; but, indeed, they also fan it. Thrice they walk round; for three (in number) are these worlds: by means of these worlds they fan it. Thrice again they walk round,--that amounts to six, for there are six seasons: by means of the seasons they fan it.
- But, indeed, the vital airs depart from those who perform the fanning at the sacrifice. Nine times they walk round; for there are nine vital airs: vital airs they thus put into their own selves, and the vital airs do not depart from them. 'I will urge the seed-layer, urge thou the seed-layer!' (the Mahiṣī says);--seed, doubtless, means offspring and cattle: offspring and cattle she thus secures for herself. [Vāj. S. XXIII, 20,] 'Let us stretch our feet,' thus in order to secure union. 'In heaven ye envelop yourselves' (the Adhvaryu says),--for that is, indeed, heaven where they immolate the victim: therefore he speaks thus.--'May the vigorous male, the layer of seed, lay seed!' she says in order to secure union. - Satapatha Brahmana, Madhyandin branch, Kanda 13, Adhyaya 2, Brahmana 8