I found this explanation at Smithsonian:
National Geographic‘s Ed Yong reports on the finding:The bit that actually changes colour is the tapetum lucidum or “cat’s eye”—a mirrored layer that sits behind the retina. It helps animals to see in dim conditions by reflecting any light that passes through the retina back onto it, allowing its light-detecting cells a second chance to intercept the stray photons. The tapetum is the reason why mammal eyes often glow yellow if you photograph them at night—you’re seeing the camera’s flash reflecting back at you.Reindeer eyes, by default, are gold. But during the long winter, their pupils dilate for months on end, Yong explains. All of this effort takes a toll on the reindeers’ eyes, which begin to swell and in turn exert pressure on tapetum.This layer is mostly made up a collagen, a protein whose long fibres are arranged in orderly rows. As the pressure inside the eye builds up, the fluid between the collagen fibres gets squeezed out, and they become more tightly packed. The spacing of these fibres affects the type of light they reflect. With the usual gaps between them, they reflect yellow wavelengths. When squeezed together, they reflect… blue wavelengths.The wintery blue, Yong writes, is about 1,000 times more sensitive to light than the summery gold. The latter color, on the other hand, helps in the summer by bouncing the majority of light off of the animals’ eyes, effectively acting like a pair of natural sunglasses.
You learn something every day.