I have a 1996 ford taurus my car will not start in cold weather

change the thermostat, sounds like it could stuck open and wont allow the engine reach operating temp, also test the constant control relay module located to the right of the battery as your facing the front of the car, also test coolant temp switch it might be defective and producing a high voltage that would cause the fans to constantly operate no matter the temp. Hope this helps

have battery and relays tested --leaning toward battery fault

Battery is dead ... dropped a cell ... get a new one ... the cold weather is hard on poor old batteries

2 possibilities
* crank sensor
*catalytic converter plugged

Spray some starting fluid in the intake Manifold this will give it a jump. Good luck

How old is your battery? If it is the original 2006 battery now is the time to replace it. A battery needs to be replaced after about 4 winters. Cold weather reduces the battery capacity and makes it harder to start. If you wait the car may not start at all.

Get a new battery - I did and it works OK.
Make sure it is the high output type as used in Jeeps etc. Check spec book for it in shop.

alternator

Check the Belt Tension. If it is even just a little loose it could cause this Problem.

I had this problem with my 98 taurus i tried jumping it wouldn't start, mine was the fuel pump check.