Should I be concerned that my accelerator stuck when it was cold

could be low float level, low pump pressure/supply
blocked fuel filter
when cold the engine is running on choke setting which draws more fuel from the carby
when it is warm the choke is off and if you have a flat spot ( (sputter) , that indicates a lack of fuel or maybe a bad accelerator pump or power valve
if the carby is a holley then replace the power valve and overhaul the accelerator pump.

Yes. The actuator motor can get stuck on the transfer case. You could wait for warmer weather or try tapping on the actuator with a hammer, lightly, to get it to disengage.

Could be the neutral safely switch is still not adjusted properly. With your foot on the brake and the transmission in neutral, move the shifter a little bit in either direction while holding the key in the start position. If the starter engages, the switch needs to be adjusted.

There is a setting for the engine called a "cold start sequence". This is activated by a cold signal from the water temperature sensor. If this sensor is stuck on the HOT setting the engine will not go into the sequence.

Some engines have 2 sensors with one operating the dash gauges and the other working the engine controls.

Some can be changed when the engine is cold without much coolant loss others you would need to catch drainage.

I had a similar problem in the winter. On very cold days the doors would be difficult to unlock, then when they were closed they would not latch. I tried using a screwdriver to move the latch, but that would not really work. So I sprayed them with wd40. That worked sometimes, but wd40 has a tendency to gunk up when really cold. So I bought some silicone spray, worked great, even in sub-zero weather.

then the normal suspects are...
IAT (intake air temp) sensor
IAC (idle air control) motor
dirty/corroded connections

do you see any specific weather conditions before/during the idle concern like cold and/or rain?

Hi
Surging is usually a vacuum leak, look around to see if a vac hose was knocked loose during the sensor installation.
Start your car and let it idle.when it starts doing its "thing" turn the heater/ ac selector to off.However for further advice clean all the sensors free from soot, starting with the MAP sensor, then to the 02 sensor, and the idle adjustment valve. disconnect the battery prior to it so that no voltage spikes may damage the ECU.
check the ignition timing if it is set to the specified degree. Next, check the idle valve to make sure that the proper engine speed is reached while idling.Adjust the throttle cable settings to get rid off the slack. After doing so, the RPM should seem great.The engine should come to life and almost straight to the specified RPM.
For hard starting in cold weather.. Try using a winter oil (5W-xx or 10W-xx) and run a tank of super unleaded through it.
OR
run gas line antifreeze in tank if it's really cold, also if you have fuel injection it may be a faulty temp. sensor, if it's a carburated vehicle it could be the atomatic choke not working as it should, but yeah 5w30 oil is good for the cold season
Thanks for contacting fixya.com

There is a cold start valve srpay extra fuel at the start to assist the start in the cold weather. If it is not open during the start then this is why there is a problem. This valve is operated by an electric coil. Even checking the resistance reading, but the valve is still not opening due to being stuck. Power is only coming to the valve during the start and the temperature is cold reported by the coolant temperature sensor . If the coolant temperature sensor is bad reporting warm temperature then the valve will not open. The temp sensor is less expensive than the valve, so it is an economical way to tackle the sensor first. Good luck.

This throttle body has a TPS ( throttle position sensor) and a Accelerator pedal sensor on it. The TPS is on the drivers side and the APS is on the pass side of the throttle body. When this happened your check engine lite came on then went off when it warmed up and acted normally. The code is still in History codes. Check it with a scan tool. I foget the code number but if it come up with the APS code in History, replace that sensor....not the TPS. It is a sealed sensor that gets moisture in it when the seal deteriates and it freezes in very cold weather.

You will need to replace the ignition lock cylinder, one of the pins that code the lock is stuck or broken. Have the new cylinder keyed to fit your original keys, the dealer or a local lock smith can do this for you.