I don't believe there is Cold Brewed at Disney Starbucks because of the volume.
Even my local establishments cannot keep up with the demand, so doubtful Disney locations can either.
Funny, just yesterday I ordered a Cold Brewed at about 2pm and after paying for it was then informed they had run out. My money was refunded and I then tried the 'new' menu item of a Caramel Granita - not as sweet as a Frappuccino, but sweet enough when it's for free!!
Also, in the Florida heat, unless using flavored (i.e.,) coffee ice cubes, any beverage served over ice will dilute while walking around. Just a thought.....