First, we see objects because light strikes them, reflects off them, and enters our eyes.
Second, we see colors because the wavelength of the reflected light differs depending on the color.
However, white light is a little different from ordinary colored light. This color is visible when all wavelengths of light are reflected.
Therefore, snow appears white because the small size of the snowflakes causes light of various wavelengths to be reflected diffusely here and there, and all of these colors blend together.
It may seem a little strange that light of various colors can become white when they are combined, but please remember that light has such a property.
This is the same reason why clouds in the sky and shaved ice look white.