As the O/P refers to a drop in natural gas pressure, rather than a complete absence of supply, I consider it likely that extreme cold weather caused both the power outage and an increased gas demand, beyond that which the pipes were sized for.

That is the power outage did not cause the drop in gas pressure, but both resulted from the cold weather.
Natural gas is normaly transmitted in bulk at high pressure, pumped by gas turbine engines.
Nearer the point of use, the pressure is reduced by means of automatic regulating valves, to that supplied to consumers.
No grid power is normally required.
As the gas passes through the low pressure pipes the pressure drops slightly. If the pipe is undersized or the demand exceptional then the pressure drop will be greater and could prevent correct operation of some appliances.

It might be worth contacting the gas supplier and asking if this has occured recently or is likely to occur.