A layer of snow only weakly absorbs sunlight, but scatters it strongly. Most of the extinction is due to scattering of the light back out of the snow and into the atmosphere. Along with the very weak absorption of photons by grains of ice, this explains why the snow appears white. The reason why it also appears bright has to do with optical depth. The average distance a photon travels before it is scattered is called the scattering mean free path.
Optical depth is measured in units of the mean free path.
On average, the photon will be scattered by the time it traverses a distance of just one mean free path. If it avoids scattering over one mean free path, the odds favor scattering by the time it traverses another mean free path, and so on. The likelihood that a photon will traverse multiple mean free paths without scattering is equivalent to the likelihood that a coin will continue to come up heads after multiple tosses. Thus, if a medium has an optical depth of four, this means that there is only a slim chance that the photon will pass entirely through the medium before being scattered. Long photon paths without scattering and long strings of successive heads on a coin toss are highly improbable.