Hypothermia does provide some protection against hypoxia-induced brain damage. However, exposure to air at -13C for only a few minutes is very unlikely affect your core body temperature enough to cause hypothermia. And anyway, the time taken to fall from 15km to a more tolerable altitude would probably not be long enough to cause that type of damage in the first place.
I'm no expert, but I seem to recall that cold limits the damage from hypoxia.