Learn Russian: Мы видели коров в поле.

The verb видели (saw) requires the Accusative case for its direct object. For animate plural nouns (like animals or people), the Accusative plural takes the exact same form as the Genitive plural. The feminine noun корова drops its -а to form the Genitive plural коров. Because cows are alive, we use this Genitive form for the Accusative.

Are animals always considered 'animate' in Russian grammar?

Yes! In Russian, anything from a human down to an insect is grammatically animate. Because of this, plural animals will always have their Accusative case match their Genitive case, just like in this sentence. (Note: Plants and trees, however, are considered inanimate).

If we saw inanimate objects in the field, would the grammar rule be different?

Exactly. If the plural object is not alive, its Accusative plural simply matches the Nominative plural (the standard plural form). If we saw 'tractors' instead of cows, we would say Мы видели тракторы. We only borrow the Genitive plural form for living things.

Why didn't поле (field) change its ending after the preposition в?

It actually is in the Prepositional case here to show location ('in the field'), but it just happens to look identical to its dictionary form. For neuter nouns that already end in -е like поле, the Prepositional ending is also -е, so the word appears unchanged.