They're cute
A running gag throughout the
Animaniacs series is the question of what animals, if any, the Warners are meant to be modeled after. The series' other characters are cartoon representations of various animals such as mice, birds, monkeys, and squirrels, but the Warners are intentionally ambiguous. Various characters in the series question the Warners about this and refer to them as a variety of different animals, frequently "puppy children", owing to their ears and tails or sometimes
Toons because of their 1930s appearance. When asked what they are, most often they state, "We're cute!" The Warners themselves often use this ambiguity as a source of humor; in one episode an entire musical number is devoted to guessing their species to which they declare "what we are dear Doctor—is cute!"
So im guessing a mix of dog an cats