My wife's 1993 740 wagon is acting up - it doesn't like the cold.

A few weeks ago, we had a super-cold day and her car was very hard to start. After starting, it ran very badly/rough, as if less than all 4 cylinders firing.

The plugs were heavily fouled and it needed a tune-up anyway, so we did all that. New plugs and wires, distributor cap, etc.

The car ran great for a few weeks, until we had another super-cold day, and the same thing happened again. Hard to start, running very rough, fouled plugs.

It seems to do fine as long as the temperature is in the teens or twenties, but if it gets down near zero, it kicks off this problem.

So, my question: What would make this car foul its plugs so badly, but only on very cold days?

Mechanical Level Alert: I have worked on 60's and 70's era cars quite a bit, but I get a little hazy with computers and fuel injection and so on. Use one-syllable words and speak slowly, please ;)

My '89 240 was doing this and would not start when cold due to fouled plugs and it was due to a bad Oxygen sensor. When the car was running it would be running rich and leave deposits on the plugs and then when I went to start it, when it was really cold, the plugs would be too fouled and the foulage wouldn't burn off right away so it would run really poorly until stuff burned off the plugs or it just wouldn't start no matter what. I wasn't sure if it was my 02 sensor so I adapted a new $16.00 bosch one wire one to see if it ran better with that and it has run so much better that I have kept the adapted one on the car for now.
Don't know if this could be your problem or not, which is why instead of spending possibly $150.00 on a new 02 sensor I would recommend trying the cheap one to see if it makes a differance. You could also test the voltage from yours with a digital multimeter which I don't have. If you do take the 02 sensore out make sure the exhaust system is warm to aid in removal and you can borrow a removal tool for free at autozone.
I then ran a bottle of Chevron fuel cleaner with 'techron" through the system and it had noticable effects.

I do have a multimeter. How would I use it to check the O2 sensor?

Also, where do I look for the O2 sensor? (Remember what I said - most of my mechanical experience is in 1960's cars...)

The 02 sensor will be screwed somewhere into the exhaust system. It will look somewhat like a deep socket screwed perpindicular to the exhaust pipe. Mine was down under the car right in front of the Catlyitic convertor facing inside. Some are up under the exhaust manifold. 240's have a thick green wire on the firewall, passenger side, that runs next to all of the other wires routed there and then it connects to a black rubber boot that conncects to a smaller black wire that will run to the 02 sensor. So try and find the green wire, I can't imagine they changed the setup from 240 to 740, it would look like around an 8-10 gauge wire size, or trace down the exhaust system from the manifold until you find it and then trace the wires back. Yours should have three wires coming off of it. The wire that connects to the green wire is the one with the signal that you can test. After the car has run for at least three minutes the sensore should be generating, I don't have my manual in front of me, around 0.4 volts to a little over 1 volt, and should constantly fluctuate also change the throttle when reading to see greater fluctuations.
My analog meter can't read the signal so I just went ahead and put in the inexpensive model to see if it worked and it did. The other two wires on these sensors are just to preheat the 02 sensor and in my opinion are not very important. You will need a special socket to remove the o2 sensor as the socket will need to fit over the wires.
Hope this helps, let me know if you have any other questions about it.
Does your car have the onboard diagnostic computer? The one where you just press the button and it blips any trouble codes to you?
Do you have any manuals for the car?