My car runs, but nothing electrical will work.

The battery light should come on when the ignition is switched on but engine not running, start the engine the battery light should then go out or the alternator is not properly charging and will not replenish the electrical energy stored by the battery. If the battery light comes on or glows dimly while the engine is running the charging system is compromised. Have the battery charged and tested, the fan belt tension checked and the charging system tested. If you have a volt meter with the engine running voltage across the battery should be approximately 14.6 volts.

Cold weather taxes weak batteries, so those two things coinciding would make some sense. When was your battery last changed? If it's old, the most likely cause of these symptoms is a weak/old battery that needs to be replaced.