The question is not well defined. However, according to my understanding if the system is not designed to operate in high voltage the system can be severly damaged. Even it can blow up.
If I assume that the system design is to be scaled to high voltage then the frequency does not get changed. You have to maintain the same frequency.
The natural conditions have very little effects on operating frequency.
To keep V/f ratio constant(designed flux density) with increased voltage on HV side, more than tolerance, with same operating frequency the system losses would increased, and would reduced the system efficiency.....
Firstly, the dynamic power consumption of a digital system is quadratically dependent on the VDD (p = C.VDD^2). You increase the voltage by a factor of m, increase the dynamic power consumption by m^2. In terms of performance, it depends on the design you are talking about. But one simple and intuitive way that both previous answers fail to capture comes from simple circuit analysis. Node capacitances are (almost) independent of the voltage. On the other hand, an increase in voltage means a better drive strength hence a quicker charge/discharge of capacitive nodes. That means a circuit MAY run at a faster frequency. So that is the good old performance-power trade-off.
Your question is super vague though. If you meant re-desigining the same circuit for a higher voltage it's a whole another story. That's because flip-flop setup-hold (SH) times (and their variation) strongly depend on the supply voltage. SH do affect the CK-to-Q delay in flops. That essentially means how fast you can run a DFF. This speed eventually has system level performance implications.
Secondly, a circuit's behavior STRONGLY depends on the environment. That is why there are spice cards for -40 celsius to 125 celsius. That's a very complex issue but I think we can summarize the temperature-dependent effects this way: Higher circuit temperature means more scattering of electrons in your interconnects and transistor channel. If they scatter more, they are less likely to make it to the other end of the (semi)conductor. That means a slower circuit. That is why cryogenic (lo-temp) design approaches are very different from the user electronics; cryo military circuits are designed to operate at higher frq's w/ more precision.