Horsy?
Equus? Steedy? Caballus?
Harmonious?
Ponish?Pony-ish? Pony-like?
I think they would use pony-like, or a similar word. If you’re pony-like, then obviously you are cheerful, helpful, friendly, everything that a pony is and what a pony should be.
They may even use it for things like, cool or nice, like, “That’s a very pony-ish decoration.” Kinda how you’d say “Smurfy”. Not that the word forms are anything similar.
There are probably some uses that can not be matched. For example, you may say “humane treatment” not in the sense of “the best possible treatment2 but as in “the bare minimum you should always expect”. And I don’t think they1d say that, they’d use words like, say, “merciful”. Acting like a proper pony is a different or higher standard than acting like a proper human.
Just my two cents.