When the whole mane is shaved off, it's called 'hogging.' This is often seen in the sport of polo. However, when it's just clipped off behind the ears that's called a bridle path and is done simply to get the hair out of the way for a bridle, making a neater appearance.
a bridlepath :)
A Bridlepath
When you clip or shave the section of mane behind the horses ear, it is called the bridle path. It is on www.Howrse.com riding level 2.
Bridlepath
Bridlepath
Bridlepath
A Bridal Path.
The bridle path
It is called a bridleway
It's called the bridle path.
WeIrD LOL
If you are talking about shaving about a 1-inch section of mane behind the horse's ears, that's called a bridlepath. It is the area that the halter or bridle sits on.