Jack London wrote that dogs show their neck as vulnerability equates to approval/affection. Showing their bellies one would imagine same principle and certainly seems like play fun for them.
My dad- who worked with horses part and full time at points in his life, said to greet a horse by, most importantly, not staring (which is distinct predator behaviour) and by showing your neck, eg tilting your head back and to a shoulder. I later learned breathing out heavily through your nose greets a horse. They use breath scent to ID other horses, & incl others of different species. Probably can pick up meat eaters that way? IDK.
But it's true if you watch, horses do a lot of nostril breathing when they meet you or another animal, and it's not
per se alarm on their part, apparently.
I'd have thought as herbivores they'd have modest sense of smell abilities as they don't track things like a canine or feline, but up close at least they utilize scent.
This is "AFIAK" and I might have been guided wrong. Haven't checked it out.
Don't get to greet a lot of horses anymore. Even fewer tigers.
