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.