I recently moved from NE Ohio to extreme southern Nj - at the tip of a 20 mile long peninsula. I have gas heat and a gas stove. A friend at work tells me that some years ago, during a very cold winter, the power went out for many days and gas pressure dropped to the point of making some furnaces and appliances inoperable. Does this sound reasonable? Also, I'm not sure if the situation had anything to do with living, literally, at the end of the line. When I lived here 25 years ago I recall a fair amount of power outages but we had an all-electric house and didn't worry about adequate gas pressure. Note: I know I'm being paranoid but ...

I don't know what you guys have down there, but up here the natural gas grid is fairly independent of the electrical grid. Seems that when you have natural gas right there in the pipe, it's considerably cheaper and more efficient to run a good ol' GE turboprop off natural gas to drive your pumps/turbines, and these generate plenty of auxiliary juice to run the electrics and control systems in your facilities, so why rely on coal-fired stuff that's two hundred miles away and three times the price per kW? Bottom line, I've lost electrical power for many long hours, but I've never heard of a gas pressure drop. YMMV.

I've never heard of gas going out but I suppose, as with any infrastructure system, it is possible. I do know that when an acquaintance who lives in the hills got municipal gas he kept the old propane tanks and has maintained them as a reserve. He keeps them filled but closed off from the house with a valve.

Closer to home I keep a small propane heater that will run off two pound bottles handy. It isn't much but worse case failure of other power source/s I can retreat to a single well insulated room and keep it warm. Redundancy is a good thing.

A small and very well insulted room, preferably an interior room, can often be kept reasonably warm with candles, small oil lamps, and body heat if all else fails.

With natural gas it's pretty hard to keep a meaningful reserve. Methane doesn't conveniently liquify like propane and butane. That's the main reason why it isn't our primary transport fuel. Yet.

A lot of places (including homes and some hospitals) now use natural gas as their preferred fuel for running generators in power outages. This means they rely upon it, which in turn means the natural gas companies have to be able to deliver during power outages.

With this is mind, it depends on your individual utility provider. I would give them a call and ask what preparations they have in place in case of a power outage. Sometimes they don't like to give that info out, but if you explain that you were thinking about running a natural gas emergency generator and wanted to make sure it would work effectively, they might be more forthcoming.

I know, for example, my local gas company installed four turbine based electrical generators in 2007 specifically to provide backup power and to reduce their electrical consumption costs.

Also, one thing to keep in mind, regardless, is that...pipes break. If a natural gas line that feeds your house ruptures, than your service will be interrupted until it can be fixed (just like if a power pole gets knocked down and takes out your electric lines). Therefore, it's best to have multiple methods of lighting your home, cooking your food, and keeping yourself warm available to you. You never know when you might loose all your utilities due to some kind of freak disaster (earthquakes are good for this).

Now if only I could afford a turbine driven generator for home...

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.

I think Adam2 has the explanation covered. Power outages normally don't affect the gas compressors for the big transmission companies, so unless there is a physical break in a line, the natural gas should keep flowing. So, if the gas supply wasn't adequate, it was likely due to high demand causing low pressure.

Adam2 does bring up an important point about low pressure. Many preparedness-minded folks install natural gas-powered standby generators at their homes, but higher capacity models may require higher-than-normal gas pressure to provide their rated generating capacity. I think in most power outages, the pressure should be adequate, but maybe not in all situations.

Of course, if the pressure gets low enough that even your stove doesn't work, that's pretty serious if you're depending on using your stove, a gas fireplace, or getting hot water.

Please correct me if I am wrong:
Some gas appliances might have to be lit and re-lit manually if there is an electric failure. E.g. my oven and stove top burners. Other gas appliances might have safety devices which fail closed if power is absent. E.g. my hot water heaters: I can re-light all day long, but unless there is electric power to the shut-off... it shuts off. So... while I consider natural gas an important preparedness addition, I don't think it would do anything for me except run the stove/ovens.
ALSO: I think the burner jet sizes for natural gas differ than for propane. So don't assume your propane bottles will run your natural gas appliances without some modifications.

All my natural gas appliances (hot water heater, space heater) run independently of electrical service. Maybe there are some new appliances that might be interconnected, but i would think that a step backwards. I do have an electric stove, but that is backed up by a propane barbecue and numerous camp stoves.