It is well known that water at 4C is denser than water at 0C. This is the usual explanation for why a body of water freezes from the surface (also it's because ice is even less dense, but that's beside the point).
So let's consider a body of water that has recently frozen over. I imagine, that nearest to the ice crust the water is at 0C and as one goes downwards, the temperature rises up to 4C (until we get close to the lake bed where the ground is a heat source). This implies, that there is a particle density gradient (higher particle density at the bottom) and a temperature gradient (highest average kinetic energy of particles also at the bottom).
But if that is the case, there must be a flux of water molecules directed upwards.
As per Floris' suggestion, I include here some reasoning behind this.
The kinetic energy of a water molecule at 4°C is higher than at 0°C by an amount that corresponds to a height difference of 200-300 meters. One would expect this extra kinetic energy to easily overcome the gravitational potential.
Of course the above treats liquid water like an ideal gas, which is obviously invalid. An explanation came up, that as a molecule moves to a region of lower particle density, it has to break hydrogen bonds and loses energy on this process. However, this is not correct. Hydrogen bonds are the reason for a lower density of water at 0°C. Moving to a region of lower temperature is favorable, as more hydrogen bonds should be formed, lowering the overall energy.
My intuition suggests, that hydrogen bonds inhibit the motion of all molecules, warm and cold and prevents mixing in general, much like two regions of a solid crystal do not diffuse into each other. This might allow hydrogen bonded clusters of molecules to act somewhat like macroscopic objects.
But if hydrogen bonds play such a role, shouldn't the energy gained by moving to a region of colder water still drive mixing?
END OF EDIT
The original question read:
So why is it, that water seems to obey the macroscopic laws of Archimedes' principle, rather than rapidly mixing, as a microscopic analysis would seem to suggest?
After the discussion in the comments (outlined in the bullet points above), I am looking for a more detailed microscopic description. Though hydrogen bonds are clearly the main player here, as the 3rd bullet point says, there's energy to be gained by moving to a region of lower temperature. Perhaps there is a potential barrier to overcome, i.e. a molecule first needs to break some bonds, before moving and forming even more of them, but how big then is that barrier?