whicker
Soft equine greeting
Whicker is what horses do when they make a soft, breathy, low-pitched sound—gentler than a neigh or whinny, often used in greeting or anticipation.
A horse might whicker when it sees its owner approaching with feed.
The word works as both noun and verb: The mare gave a soft whicker as I entered the stable.
It's sometimes used figuratively for similar sounds, like a quiet laugh.