Why are so many different types of objects white, yet appear gray when they are wet? There are many things with different textures that appear white – salt, beer foam, paper, shaving cream, snow, talcum powder, white paint, etc. The most common answer is all of the frequencies must be reflected in order for us to perceive white, which I already know. There must be more underlining details why such a huge variety of things are white. Furthermore, if you wet paper, snow or talcum powder, they appear off-white or gray. Why is this?
 A: If I read your question correctly, it centers on what is the cause of objects to be opaque and white.  There is a common thread through salt, beer foam and talcum powder – all of these objects have embedded in them transparent particles. For example, if we look at salt, at its “smallest scale” are transparent particles called grains.  If the transparent particles are small but larger than the wavelengths involved, light entering each transparent grain will act as a scattering center. That is, light will get reflected and refracted, and will reemerge with its frequency unchanged. That’s why the object appears white but it doesn't explain why it is opaque.
Its opaqueness comes from the fact that there is a change in index of refraction from air and salt’s transparent grains. The amount of light that is reflected is given by its reflectance, which in turn is determined by the differences between the index of refractions ($n_1 =$ air and $n_2 =$ salt). When light is at normal incidence, the reflectance is given by 
$$R=\frac{(n_1-n_2)^2 }{(n_1+n_2)^2}$$
The larger the change in the two indexes ($n_1−n_2$), the more light is reflected and the material will appear more opaque. For optical frequencies, the index of refraction for salt is 1.54 and its reflectance off one surface is R = 0.04. However, a salt pile is made with its numerous pieces of salt crystals that will reflect light off of numerous surfaces, increasing the number of reflections back into the incident medium.

Therefore, the reflected light reaching the observer will be white and opaque.
Now we can apply this to water vapor or beer foam, snow (ice crystals), paper (transparent fibers) or talcum powder (crystal) or even ground glass, each of which is composed of transparent particles. 

So white light is reflected off of multiple surfaces with its frequency unaltered, they will appear white and opaque. As for white paint, I am guessing here, but I expect that white paint is composed of small clear transparent particles floating in a clear adhesive so that the paint will stick to a wall when painted. 
The question of why paper, snow or talcum powder appears off-white or gray must be due to the reflectance decreasing for the material since less light is being reflected. This makes sense because a material getting wet is now surrounding the transparent particles with a higher index of refraction; that is, the incident medium goes from air to water. The key point being that it’s the difference ($n_1−n_2$) that determines how much the reflectance decreases (see the above equation). For example, I assume that snow has an index of refraction of ice, $n_2$(ice)=1.30. Since $n_1$(water)=1.33, the reflectance dramatically decreases for wet snow to R(wet snow)$=1.3×10^{-4}$! This dramatic decrease implies that a lot more of the light is getting through and not reflected, therefore, its gray look. So if water surrounds paper or talcum powder, it is the reduction of ($n_1−n_2$) that leads to objects appearing off-white. This was my favorite part of your question and the reason why I answered it. Great question!
A: When you wet white things they appear darker because wetting them causes them to clump together, and there is less surface to reflect light.
