Born is dean of faculty.
Academy officials were treating the incident as a "teachable moment," said Lt. Col. John Bryan, a school spokesman. He said he did not know of any plans to discipline cadets.
Brig. Gen. Gregory Lengyel, the commandant of cadets, said in a statement that the brawl was unacceptable.
Lengyel did not say how many cadets were involved but said it was a "relatively small number."
The ritual is called "First Shirt/First Snow" and involves freshmen trying to throw cadet first sergeants known as first shirts into the snow.
"This ritual has devolved to become increasingly violent, with significant numbers of cadets requiring medical care over the past two years," Born wrote in her email.
"What used to be [freshmen] throwing the first shirt into the snow has turned into a brawl between upperclassmen defending the first sergeant and the [freshmen] trying to capture the first sergeant."
It wasn't immediately known how many cadets were injured last year.
"Obviously, this has gotten out of hand and cannot be repeated," Born wrote.
Born wrote that Lengyel stopped short of banning the ritual and said cadets could propose keeping it if they found a way to avoid violence.
The academy is located outside Colorado Springs and has about 4,000 students. Upon graduation, they are commissioned as second lieutenants in the Air Force.