I'm a relatively new brewer, but I'm wiling to give a description of what solubility and colloids are. For the sake of simplicity, I'll assume water is the solvent.
From a practical sense, a substance is soluble if water will form a hydration shell around it. At a molecular level, this usually occurs because there are enough polar sites which are able to hydrogen bond with water. Things like carbohydrates, most proteins, and ions are all soluble to varying degrees in water. Most lipids are generally insoluble in water due to their relative lack of polar groups.
I'm not really going to try and get into a detailed discussion on the physics of what really drives solvation, because it requires a rather subtle and complicated discussion of entropy and how it relates to the Gibbs free energy of a particular reaction. Suffice to say that, if the most energetically favorable configuration for a compound in the solution is to be surrounded by a bunch of H2O molecules, then that is what will occur. Solubility for a molecule is, in general, a function of several variables, temperature being one of them.
As to the discussion of whether a mixture of beer and yeast is a solution or a colloid, I would submit that it is neither. One of the defining characteristics of a colloid is that it doesn't settle, so by inspection we can see that is clearly not the case here. I suppose that one could make try to make the case for yeast to be dissolved in water, but that also doesn't explain the fact that eventually, the yeast will form a layer at the bottom of the container.
It's probably most accurate to look at the yeast / beer mixture as a suspension. The insoluble yeast cells appear to be dissolved because one can't seem them without a microscope. However, given a constant temperature, no turbulence or convection in the fluid, and eventually, the cells will sediment. You can see this phenomenon with liquid yeast vials as well as the carboy after a week or two of fermentation. The reason that the yeast cake hardens like a previous poster mentioned is probably because water molecules trapped in the yeast cake eventually escape, although that is just a guess. Also, keep in mind that there is 5 gallons of dense liquid on top of it, so after a while, the force of the fluid above it compresses the yeast cake into a rather compact state.
Another example of this is blood. Blood is a suspension of erythrocytes (red blood cells), leukocytes (white blood cells), and platelets into which proteins and other macromolecules have been dissolved. If you take blood and put it in a centrifuge (or let it sit a long, long time), it will form three primary layers: the hematocrit (the red part), the buffy coat (the white part), and the plasma, which is the straw-colored solution that remains on top. Note that, during centrifugation, the red blood cells get pulled out of suspension, but the layer of dissolved substances (mostly proteins) remains a solution. The same thing happens to beer, it just doesn't need a centrifuge to get all of the particles to drop out of suspension.
I'm going to lean over the plate here and proffer a hypothesis on cold crashing. My suspicion is that cold crashing beer accomplishes the same thing that centrifugation does for blood, which is namely to separate the insoluble particles (yeast, particulates, etc.) from the rest of the solution. The drop in temperature probably aids in this by reducing the overall kinetic energy of the molecules in the liquid and accelerating the rate at which particles drop out of suspension. I think that if one were to allow the beer to sit for an exceedingly long time, maybe a year, the result would be the same - as far as the suspension goes. No doubt the taste would be affected, which probably explains why cold crashing is practiced.
One final thought - as a previous poster mentioned, solubility is also a function of temperature. So, in addition to accelerating the rate that particles drop out of suspension, it's entirely possible that dissolved proteins, sugars, and other soluble compounds would also be forced out of solution as well. So, it wouldn't surprise me to find that, after cold crashing, the yeast cake has all sorts of soluble bits in it as well.