The practice of holding one nostril while simultaneously blowing out the other. You would usually lean over or away from your body so as not to blow snot all over yourself.
This saves one from nastying up one's sleeve(s). Since the Amish live a simple life they wouldn't have fancy store bought Kleenex.
"Dad's allergies were bothering him so bad while we were hiking he had to use the Amish Kleenex."
"I sneezed so much I used up all my tissues and had to use the ol' Amish Kleenex"
"I had to resort to the Amish Kleenex since it was Summer and I was sleeveless."