It's not the 02 sensor-- the signal from the O2 sensor isn't useful until the sensor reaches a particular temperature range, so it isn't used in the fuel/air mixture enrichment feedback loop until the engine is warmed up.

The biggest risk with a malfunctioning O2 sensor is that the car will run rich and ruin your catalytic converter. I've done 02 sensors in the driveway in winter here on the other side of Lake Ontario. Just give the sensor a small shot of good penetrating oil (P'Blaster or Kroil, not WD-40) for a few days before you do the job.

Good luck!