Hard starting: Coolant Temp Sensor?

[sleepydsm]

When my car is cold, it is extremely hard to start. I crank it over, doesnt want to fire. I tap the gas pedal very quickly, and it will start to sputter. Eventually, by doing that, the car will fire and if I stop quickly tapping the gas pedal the car will die. Once I get driving, the CEL comes on for "Coolant Temp. Sensor." Once the car reaches operating temp, it drives perfect.
On my logger, with the car cold, the coolant temp is -12 or -15. After inspecting the harness lead that plugs into the sensor, I noticed the wires were a bit frayed, so my friend popped out the connectors, and resoldered new wires in there. Today I reconnected them (and they are hooked up as they were before), and it still is hard starting. So I figure it must really be the sensor itself.

Could a bad coolant temp sensor be causing all this?

I assume maybe because the ECU doesnt know if the car is cold or hot, that it adds too much fuel and thats why it won't fire.

Thanks for your help.