Four things must happen to make water white

Agitated water at the air interface encourages aeration of liquid water with air bubbles. When there is turbulent water, several things take place simultaneously:

• Water dissolves some of the air 
• The churning water creates air bubbles and air pockets in between the water molecules

Turbulent water  creates an environment where air bubbles and water mix together. The gasses within air (Nitrogen, oxygen, carbon dioxide) do not absorb light; they reflect it.

A disorganized mass of air bubbles held in place by water will reflect light. Since none of the light is absorbed, the light reflected back is pure white.

Keep in mind that it is the air bubbles that reflect the white light back.  It is not water bubbles or water droplets.

For example, a multitude of air bubbles produced by scuba divers will show up as white. When the production of the bubbles ceases, the white color dissipates. 

Have you heard the expression "foaming at the mouth"? Colorless  saliva turns white as breath is forced through the liquid in the mouth. The result is white foam bubbling or spluttering out. 

For some animals, like dogs, frothing saliva could be a sign that they are anxious or overheated.  A combination of panting, hyperventilation, and excess saliva will lead to air-bubble-laden frothy and white saliva.

Snowflakes are frozen water. When snowflakes fall and collect on the ground, they glue to other flakes through frozen hydrogen bonds between the water molecules. In doing this, they entrap pockets of air. 

Whereas a few snowflakes are colorless, a mass of snowflakes with entrapped air bubbles will appear white. A chaotic arrangement of air bubbles will bounce light (refract) all over the place within the heaps of snowflakes.

Enough of this light, though, is reflected back to us from the surface of the snow as white light.

It depends on how you freeze the cubes. Household ice cube trays often freeze water relatively quickly. This entraps the air bubbles in the center of the cube - the last place to freeze. 

While the ice cubes shown below  on the left look as if they have clouds trapped in their center, it is possible to produce perfectly clear ice cubes at home.

As long as there is slow freezing from the bottom of the cube to the top,  the air is forced up and out. The result will be a transparent ice cube through which you can read print!

What about clouds? Or Fog? Or misted breath?

Clouds are a mixture of water droplets and air. What holds everything together?

Is it the liquid or the solid phase of water?

Clouds , fog, and cold breath mist are specialized cases of white color in water. 

To have whiteness in water, four things must take place:  

1. Environmental conditions trap gas bubbles (air or other gas) within water.
2. The gas does not absorb light.
3. The different sizes of entrapped gas bubbles cause chaotic refraction of light within the medium. This prevents light from going through.
4. Enough of the light is reflected back to us through the topmost layer of gas bubbles. We see white light when all wavelengths of light are reflected back.

Liquid water entraps gas bubbles through turbulence and/or hyper-aeration of the liquid.

Frozen water, like snow and ice, hold the different air pockets and air bubbles in place through freezing of water molecules around the gas.