Why does the "snow" created in hockey play look so bright white?

Answer: Ice is a good reflector of light.

Ice is a good reflector of light, especially blue light, and ultraviolet light. This makes snow "bright". Skiers wear yellow goggles that absorb blue light, making the snow scene less blinding to the eyes. Drivers of autos also notice how bright snow is in winter time.

Snow flakes have a very large surface area for their weight. This large surface reflects light better than blocks of ice, or ice in a hockey rink, or on a pond. Light is best reflected by a smooth surface, which is the case for snowflakes. Also, the "star-like" surface of snowflakes creates a large surface area for any given amount of ice.

High-flying jet planes emit water vapor, from fuel combustion, that freezes into ice crystals. Notice how large the "contrails" of high-flying jets are compared to the size of the jet plane. The contrails are larger than the jet planes, because the ice crystals in the contrails are very far apart.

Jet contrails show that small amounts of snow can reflect a lot of light. The ice crystals in the jet's contrails are so very far apart that they reflect just one-millionth of the sunlight striking the contrails, yet they look so large compared to the jet plane.