Barbing hair/Barbing shop
"to barb your hair" for "having a haircut"
Men do say that they want to 'barb' their hair. The word 'barb' does not have anything to do with cutting at all let alone human's hair.
As a noun, it means
a point or pointed part projecting backward from a main point, as of a fishhook or arrowhead.
an obviously or openly unpleasant or carping remark.
Botany, Zoology . a hooked or sharp bristle.
Ornithology . one of the processes attached to the rachis of a feather.
one of a breed of domestic pigeons, similar to the carriers or homers, having a short, broad bill.
When used as a verb, 'barb' is used with an object like 'furnishing something with a barb'.
"barbing your hair" as an expression is not grammatical in any way.
I want to have a haircut.
NOTE: Never say I want to cut my hair.
You go for a haircut at a BARBERSHOP not a barbing saloon.