I've read in couple of sources that level of hardness of light affects color saturation somehow - harder the light more saturated colors are. Is this actually true or not?
You get strong color saturation when the colored areas are exposed as midtones. So it's exposure that determines whether colors are saturated, not the hardness of the light.
So soft light and hard light that result in the same exposure will result in the same level of color saturation.
The definition of saturation can vary a little... this is what CIE (international commission on illumination) defines it as:
"17-1136 saturation colourfulness of an area judged in proportion to its brightness
NOTE For given viewing conditions and at luminance levels within the range of photopic vision, a colour stimulus of a given chromaticity exhibits approximately constant saturation for all luminance levels, except when the brightness is very high." http://eilv.cie.co.at/term/1136
Pay attention to the note... if you can see it, then luminance does not notably affect saturation.
Technically, color saturation is the bandwidth/frequency of light from a source. Hue refers to the color of the image itself, and saturation describes the intensity/purity of that hue. Again, luminance/illuminance does not change this (other than the color of the illuminance/lighting if not full spectrum).
But what many tend to mean when they say "saturation/saturated" is what one might call the "richness of the colors" or some such; but there really is no definition of/for that... In general, this refers more to exposure; e.g. underexposing a sunset to improve the colors/saturation.
Well, if we put it too simply colors are just reflected light, different surfaces reflect light differently and human eye decodes those reflections as colors. Of course light intensity affects our perception of color: too much light(for human eye) shifts colors to white, while lack of light shifts them to black, thus color will change accordingly. Most saturated colors will get when exposure is just right, not overexposed and not underexposed but somewhere in between. There is also color of light that must be taken into consideration as color of light will shift reflected colors to lights original color. For example: Neon white lights will shift colors to cooler side, while more warmer candle light or setting sun light will shift then to warmer side.