Perhaps somewhat related to your experience, I had something very weird happen to me a few winters ago. It was a particularly cold spell we were having, and I was only driving the car for short distances to run errands and such, and then leaving it parked outside until repeating the routine the next day.
One morning the car just wouldn't start, despite cranking strongly. After several attempts, and before I wore the battery down, I had it towed to my mechanic.
What he found was quite surprising, the O2 sensor was useless because it was wet with water, which came about because the catalytic converter had filled with water, and when he drilled a small hole in the converter he out came about a quart of water. New O2 sensor and a check of the diagnostics to make sure nothing else was awry and I was on my way.
The explanation is still elusive, but somehow it seems that when the car was being driven those short distances, water vapor was generated in the exhaust but not fully expelled. When the car was shut off, and with the cold weather, whatever water was in there froze. Repeat this a few cycles and voila, ice and water buildup, inoperative exhaust, inoperative O2 sensor, inoperative car.
I'm not sure if that explanation makes sense, but it could mimic your experience.