Winter Whites coat changes because of the shortening of days. That is why during the winter, their coats usually change color, not because of temperature. I live in Saudi Arabia, and my Winter Whites do change color. The only reason why they have changed color is because when my female delivered her babies, I kept the cage kinda dark to keep it warm inside so that the babies were not cold. Most A/C's here are window units and my cages are kept in my office at home where I spend most of my time with the AC on. Sooo, to them the days seemed to be shorter and their coats started to change.
As far as the knowing if it is PURE breds, not sure how to tell.