You can leave it unplugged until you get a new one. I do suggest to be on the safe side cover the end connected to the injection pump, so it does not ground itself out.
This is what the sensor does. To comply with the exhaust emissions regulation, the timing of injection pump should be around 6 to 9 degrees before TDC. These timing values do not allow proper start-up operations when engine is cold. To ease engine start-up, a cold advance system gives to the injection pump a temporary over-timing.
When coolant temperature is below 50 C (122 F), the solenoid valve is activated and opens the cold advance circuit.
On my 5210, I did not have to drain the coolant, just made sure it was not hot at the time. I put a pan under the tractor to catch the coolant, so as not too have to clean it up.