Since snow is composed of small ice particles, it is a granular material.
It has an open and therefore soft, white, and fluffy structure, unless subjected to external pressure.
Snowflakes come in a variety of sizes and shapes.
Types that fall in the form of a ball due to melting and refreezing, rather than a flake, are hail, ice pellets or snow grains.
Once on the ground, snow can be categorized as powdery when light and fluffy.
It is also fresh when recent but heavier, granular when it begins the cycle of melting and refreezing.
Eventually ice once it comes down, after multiple melting and refreezing cycles, into a dense mass called snow pack. (source)
So can hamsters eat snow at all?
Unfortunately it is too cold for hamsters to eat and should be avoided as far as hamsters are concerned.