A regular (non-plugin) Prius will go maybe a mile on the battery alone, and only in the right circumstances. Acceleration on the battery is poor, and battery-only mode is limited to 40-45MPH. It'll start the engine for you on demand, so this is no problem when driving, of course, it just illustrates that the battery performance isn't all that important.
Depending on how you drive it, cold weather can hurt gas mileage. If you're driving in a way that the engine doesn't run much, then it may have to run the engine more to generate heat for the heater. However, if you're driving in a way that runs the engine a lot anyway (highway driving, decent amounts of acceleration hard enough to require the gas engine, etc.) then you get the same kind of "free" heat as a normal car.
Driving my Prius v, I'm battery-only basically when cruising on surface streets, sitting idle, or maneuvering around small, slow residential streets. And maybe, maybe if I'm accelerating away from a stop on a decent downhill slope with nobody behind me.
My friend here has a 2011 Toyota Highlander Hybird, and she barely notices a difference in range year-round.
The storage capacity of the fuel is not affected (much) by temperature.
From a simple perspective, the batteries in a hybrid just serve to smooth out the energy demand and provide regenerative braking.
The car has a protection mechanism to prevent the battery from freezing, and when left over night in the cold without a charger, it will actually run an auxiliary heater to keep the battery warm enough.
The reviewer expected the charge to be the same in the morning, so he called their technical support when it was so low. They didn't explain that the charge can substantially decrease overnight when parked in the cold, because it automatically runs a heater for the battery. Instead they suggested that it was an erroneous reading, and that it would correct once the battery heated up.
It wasn't really a design flaw so much as a mistake from technical support exacerbated by an overbearing response attacking a journalist for not being omniscient.