Ice is a crystalline material which means that the water molecules are regularly ordered. The surface of ice is therefore very smooth.
Snow is made from snowflakes, which are six sided.
On the ground, snow has a very irregular surface because the flakes have just landed higgledy-piggledy. Light is refracted by the smooth surface of the ice, which means all the rays of light pass through the ice at the same angle, and is therefore transparent. Snow with its uneven surface reflects and refracts light at all different angles giving a white colour.