When light shines on ice, it can do one of three things: it can be reflected back toward the source, transmitted straight through the ice, or absorbed inside the ice. These light behaviors are dependent on the characteristics of the ice.

Glacial ice, for example, often exhibits a light blue color. This is because the massive weight of the glacier squeezes out most of the air in the ice, increasing its density. Water absorbs red light and reflects blue light, which is the reason lakes appear blue. Both liquid water and glacial ice have less air in them than regular (white or clear colored) ice, and both are blue!

Dark ice, such as black ice is usually a thin ice on a dark background. In this case, most of the light passes right through the small amount of ice and is absorbed on the black background. This prevents light from reflecting back to our eyes and the ice looks dark.

In the case of white ice or snow, there is a lot of air contained between the ice crystals and this helps effectively reflects all wavelengths (colors) of light, leading to a white appearance. White light (such as sunlight) is produced by combining all wavelengths of light at the same time.

Ice is blue, but it can appear white if the crystals are small enough because the sun's light is reflecting off of the crystal surfaces, and sunlight is largely white. It's the same reason why clouds are white. If the ice is solid, i.e. no crystal surfaces to reflect light off of, then the ice will be blue.