It was the horse that threw me!
Horse tee gate, pony tee gate.
The confusion arose for me because a horses coat is always referred to as "hair" or its "coat", never fur!
Don't blame me, I don't make the rules!
From the internet -
We regard humans as having “hair,” not “fur.” And we use “hair” for what grows on livestock with thick, leathery hides—horses, cattle, and pigs.
But we generally use “fur” for the thick, dense covering on animals like cats, dogs, rabbits, foxes, bears, raccoons, beavers, and so on.
Why do some animals have fur and others hair? The answer lies in the origins of the noun “fur,” which began life as an item of apparel.
In medieval England, “fur” meant “a trimming or lining for a garment, made of the dressed coat of certain animals,”