Assuming you can keep a device in its "normal operating (temperature)
> range", how advantageous is it (think MTBF) to drive that ambient
> down? And, is there a sweet spot (as there is a cost to lowering the > temperature)?
It's generally figured that decay and degeneration proceed more slowly at lower temperatures. A popular rule of thumb is that a 10C temperature drop halves the rate.
The Arrhenius equation says it depends on the activation energy of the process, and the factor of two in 10C would reflect an activation energy of 52,900 J/mol (52.9 kJ/mol) which is pretty ordinary.
Also, is there any advantage to minimizing the hysteresis between
> the ACTUAL operating temperature extremes in such a control strategy
> (given that lower hysteresis usually comes at an increased cost)?
Only primitive (bang-bang) control schemes have hysteresis. Learn about proportional-integral-derivative control (and it's more advanced variations).