Let's see . . .
We all agree that, if an animal's sex/gender is known, we use the appropriate he/she.
Beyond that . . .
The less-domesticated animals are more likely to be "it". The closer the contact with a human, the greater the likelihood of "he/she".
Animals that have common male/female forms might well be "he" unless the female form is used, e.g. a "lion" will be thought of as male because we have the commonly-used term "lioness".
Some animals are generically thought of as a specific "gender" unless otherwise noted. As I mentioned earlier, cats are "she" and dogs are "he". The big cats (lions/tigers) and other large predators are "he". Chickens are "she". Cows are also "she". (Because we have the word "bull" to indicated the male. Incidentally for larger herd animals we can add "bull" or "cow" to indicate gender: bull moose, bull elephant, cow elephant, etc. Also incidentally, certain professions are thought of as male or female: "professor" is male; "teacher" - especially at the elementary level - is female, even though we know that both men and women practice both professions. "Nurse" is female, and we even get "male nurse" to be clear.)
Since "he" used to cover generic instances, it could also be used with animals of unknown gender/sex. This usage is disappearing. It is always acceptable to use the generic "it" with an animal (but never with a human).
This is probably more information than anyone cared to know, and I'm sure someone will express a different experience with the language. :-)