The cowl was the original head-coveing for monks East and West and remains part of the habit of Latin monastic and mendicant orders and is the headgear (along with skufia) of the Byzantine monk of the Great Schema.
But when? It wasn't there at the time of the schism, so it must have come in the last 1,000 years, possibly even the last 500 years.
Where are you getting this? St Benedict's Rule ca 500 AD speaks of the cowl:
Chapter 55: On the Clothes and Shoes of the Brethren
Let clothing be given to the brethren
according to the nature of the place in which they dwell
and its climate;
for in cold regions more will be needed,
and in warm regions less.
This is to be taken into consideration, therefore, by the Abbot.
We believe, however, that in ordinary places
the following dress is sufficient for each monk:
a cowl (thick and woolly for winter, thin or worn for summer),
a scapular for work,
stockings and shoes to cover the feet.
The monks should not complain
about the color or the coarseness of any of these things,
but be content with what can be found
in the district where they live and
can be purchased cheaply.
The Abbot shall see to the size of the garments,
that they be not too short for those who wear them,
but of the proper fit.
Let those who receive new clothes
always give back the old ones at once,
to be put away in the wardrobe for the poor.
For it is sufficient if a monk has two tunics and two cowls,
to allow for night wear and for the washing of these garments;
more than that is superfluity and should be taken away.
Let them return their stockings also and anything else that is old
when they receive new ones.
Those who are sent on a journey
shall receive drawers from the wardrobe,
which they shall wash and restore on their return.
And let their cowls and tunics be somewhat better
than what they usually wear.
These they shall receive from the wardrobe
when they set out on a journey,
and restore when they return.http://www.osb.org/rb/text/rbeaad1.html#55