In the winter, I notice whenever bodies of water (that are normally brownish) freeze, they appear to look more blue.
Not a bright blue, but a blueish tint.
Different refractive indexes.
Saying “different refractive indices” is probably correct, after a fashion, but doesn’t begin to cover it. The blue color of water and of snow and ice are different phenomena than the one responsible for the blue color of the sky. The latter is mostly Rayleigh scattering, and can be explained as a manifestation of single scattering from things n the air (mainly the air molecules themselves, but also dust, pollen, etc.)
The blue color of liquid water and the blue color of ice and snow is a multiple scatter effect that’s rarely, if ever, covered in even graduate texts on optics and scattering, and doesn’t have the short and nifty formula of Rayleigh scatter. There have been some articles American Journal of Physics that try to cut it down to conceptual size.
Don’t the seaweed & similar plants that are growing in lake bottoms die off or die back significantly during winter? And since they are mostly green & brown colors, that would change the look of the water, right?
Could it also have something to do with the fact the top layer of ice is much cleaner than the water it was made from - cleaner in the sense of having less suspended particles and dissolved substances - since these freeze out of the water? So what you’ve got looks a muddy brown in summer, but much cleaner in winter, reflecting the sky.
The dark plant matter is still down there and plenty of plant pieces are suspended in the ice. It’s the ice crystal structure that dominates how the light reflects back. A thick layer of ice will let you see all the way down to the bottom of a shallow lake too. You can see things like belly side up frogs waiting for spring, and a lot of suspended plant material frozen in the ice.