(Classical) Latin nouns have one of 3 genders (masculine, feminine, and neuter), and each noun has 12 possible forms (6 cases * 2 numbers); pronouns follow similar rules; and the adjectives modifying a noun have to agree with it in case, gender, and number (so typically a single adjective has 36 possible forms). Verbs vary by voice (active/passive), mood (indicative, subjunctive, imperative, infinitive, participle, gerund, supine), tense (different moods have different numbers of tenses, with 6 for the indicative), number (singular or plural), and person (3 persons); overall, a single verb will have more than a hundred different forms.

Because verbs have so many specific forms, it is also pretty common in Latin, as in most modern Romance languages, to omit the subject of a sentence, as it can typically be inferred from context plus the specific verb form - so, you often have to recognize the verb form to be able to understand who the sentence is even talking about (e.g. a sentence might say "amo regem"; if you recognize the words but not the specific forms, this means "love king"; but this unambiguously means "I love the king").

Now, there is quite a bit of regularity here - there are 5 categories of regular verbs (plus some specific irregular verbs), and 5 categories of nouns (though there are multiple sub-categories, as there is some variation in noun forms even in the same category; plus of course some irregular nouns).

Overall no, I don't see any comparison where you could say that Latin is a simple language. All modern Romance languages have universally merged or dropped various of these features. For example, Spanish drops the case system entirely, drops the neuter gender, and reduces the number of moods for verbs.