>>96078025
At least 2 of those suggestions are NOT serious answers, anon, they're made up silly answers.

>Big dog
Giant wolves are culturally connected to goblins. It would step on the toes of that army's identity.
>Big hog
Likewise an Ork theme
>Big cat
Closest is high elves with White Lions or the Sabretusks but they both are geographically specific and unavailable to the Empire
>Big mat
Araby
>Big gat
Mechanical steed already exists and isn't mass producible. (It uses gunpowder instead of coal, that's why they can get it work but apparently steam tanks are impossible)
>Big donkey
Horse
>Big honkey
Giants are not good mounts, they're too headstrong and expensive to maintain