There's a lot going on in this thread. I’ll try to address some of the more confusing points.
Hankelec said:
My question is; does the extreme cold have any affect upon the rate at which the electrons of various atoms in a compound, travel about the atom's nucleus?
In a sense, kind of. At nonzero temperature, electron energy is thermally distributed just like every other degree of freedom. This explains why, in a normal, non-superconducting solid, electrical conductivity generally increases with temperature, because as you increase the temperature, you increase the average number of electrons in the conduction band. It also explains why metals are generally more thermally conductive than insulators: heat energy is carried in electron motion as well as atomic motion. Similarly, in a group of weakly interacting atoms or molecules like one finds in a gas at thermal equilibrium, the electronic energy is thermally distributed, but these energy levels are widely spaced compared to thermal energy at everyday temperatures, and the electrons are therefore overwhelmingly likely to be found in their ground energy states. This is a straightforward stat mech problem, as long as your calculator is double precision (when I said overwhelmingly, I meant it

).
Superconductors are different because their mechanism of conductivity is completely different, so we'll ignore them right now.
Hankelec said:
My acquaintance with atomic structure pretty much ends with electrical conductors are made up of atoms with 4 or less valance electrons while insulaters have 5 or more valance electrons.
No idea where you're getting this but it's not right. Carbon has 4 valence electrons, but diamond is an electrical insulator whereas graphite is a conductor.
Hankelec said:
I guess my initial outside the box notion was that if electrons were to stop traveling because of total absence of heat, then the material being chilled would most likely cease to exist.
The reason this notion is fraught is because the classical idea of "motion" doesn’t carry over cleanly to quantum mechanics. At absolute zero, where all electrons in a material are in their lowest possible energy states, the wavefunction of the system does not evolve in time in any observable way, so there's no "motion" in that sense--the electrons don't really "travel," so to speak, in any observable sense. However, electrons in a solid do occupy quantum states that have non-zero momentum, even at absolute zero. Moreover, even in an isolated atom, the quantum virial theorem applies, so that there is a non-zero average kinetic energy for electrons in an atom at absolute zero. So even though the system doesn't observably change over time, components of it have non-zero momentum and kinetic energy. Clasically, kinetic energy/momentum/system-changing-over-time are basically all synonymous with the concept of motion but quantum mechanics is more complicated. Regardless, materials don’t cease to exist at absolute zero.