A considerable part of the grammar structure you are thinking of is derived from Latin language grammar books. For example, both declension and case are Latin-origin words. And we use them in English to describe what the Romans used them to talk about in Latin. So if the question is whether we have 'imposed' a grammar scheme of Latin, the answer is no, not really, we derived that grammar scheme from Latin grammarians. In fact, it's the grammar scheme often imposed post-factum on other languages, including English, generally not-that-helpfully.

There is a different question about how Romans actually taught Latin. Just because Latin grammarians talked about Latin in those categories shouldn't be taken as proof that they taught Latin in the fairly clinical and dry way they is common today, that teaching tradition owes a lot more to the influence of German philological traditions from the 18th century.

Donatus' Ars Grammatica is a good, in fact the classic, example of Latin grammar by a Roman. Quintillian's Institutio Oratoria, especially the early sections, will give more insight into Latin pedagogical education.