It's technically possible for it to snow on Mars, but the snow almost never accumulates on the ground.
The average temperature on Mars is about -80 degrees Fahrenheit, so it's definitely cold enough for water and other substances to freeze and form snow, and there is some water in the atmosphere. In fact, Mars rovers have observed clouds low in the Martian atmosphere.
But the ice particles on Mars are so small that that they evaporate before they reach the ground.
@mylesbkeating, they're smaller because they're made out of carbon dioxide rather than water, and those two substances have different structures.
Why are the crystals smaller? Drier atmosphere, less far to fall through the atmosphere, too cold, something else?