White deer do occur naturally in the wild. They are quite elusive

the lack of pigment in the coat will also change the eyes appearances.

Yes, but it would affect the color, not the shape.

the appearance of the shape though, because areas that would be brown or black are now white, it makes it LOOK different shaped than a normal eye

I'm not saying this picture is true, but white deers do exist, a few miles from where I live you can see a big herd with mixed deers with white and brown. The white ones gets more and more every year, so I guess it's some sort of mutation that spread in the herd