All languages utilize onomatopoeia without exception. It is theorized to be among the earliest forms of proto-language.

Social aspects of language use that determine prestige and formality may restrict its use in formal situations. Written language, an artificial standard, is particularly prone to this. It is not, however, unidirectional. Written standard Englishes, and to an extent media Englishes tend to view onomatopoeia as informal speech. Persian, on the other hand, utilizes a wide variety of onomatopoeic forms in both colloquial and formal context. That is, it is not considered childish or simplistic cross-linguistically to use these forms; that is determined by sociolinguistics.

As for samples from older languages, we have hundreds. A few:

• Attic Greek, The Frogs (Aristophanes): Dionysus is riled by the croaking of frogs, represented "Βρεκεκεκὲξ κοὰξ κοάξ."
• Old Latin (pre-Classical), Persa (Plautus): Sagaristo describes a whip thus: "tux tax meo tergo erit." translated by Henry Thomas Riley thus: "Crack, crack. It will be upon my back."
• Akkadian, representative of Semitic languages, can trace many reduplicated roots to an onomatopoeic source, for both nouns and verbs: dabābum 'to talk'; qa^c qa^c 'raven'.

Onomatopoeia has been analyzed as either primary or secondary - primary meaning the word imitates the sound the referent makes, such as Akk. halālum 'to whistle'; secondary meaning the word is imitative of a sound associated with the referent by a third party, such as Arabic waṭwāṭ 'bat' (the sound of the flapping wings to an observer, rather than a sound the bat vocalizes). Note that both can be either impromptu sounds, as Aristophanes's frogs make, or lexicalized forms that then refer to those animals/objects, as for the raven in Akkadian. We find both types widespread cross-linguistically both today and in the earliest records of the languages I've mentioned. It's a universal phenomenon.

As for Latin, and Latin animals in particular, the best source I know of for these is a fragment of Suetonius' De naturis animantium. It does not mention cows, but it mentions dozens of other animals. Apparently chickens crispire, while bees bombire.

Other sources:

• Wordplay and Powerplay in Latin Poetry. Mitsis, Phillip, and Ziogas, Ioannis. Trends in Classics - Supplementary Volume 36. DeGruyter, 2016.
• Gemination in the Akkadian Verb. Kouwenberg, N.J.C. Brill, 1997.