Cold engine hesitation

No CEL, I presume? If there is a CEL, get those codes pulled and report back.

I would start by looking for possible vacuum leaks. Then look at the intake air temp (IAT) and the water temperature sensor (the one on the passenger side).

How long does the hesitation last - just a couple of minutes or until the car is fully warmed up? Do you have access to a OBDII scanner that can read out the live sensor data? It may be helpful to know what the computer is seeing and if it's happening only in open loop operation or in closed loop too.

Clean MAF, check vacuum leaks, plugs

A fuel filter is unlikely to be the cause of this problem. If it were a clogged fuel filter, drivability wouldn’t improve when the motor was hot. It is a good idea to always have a clean fuel filter.

Simply because the Mass Airflow sensor is vital to a well running car, suggest cleaning the MAF. Use cleaner designed for this purpose. The sensor is delicate and easily damaged. If you have an oiled air filter then this step is very important.

The Intake Air temperature (IAT) sensor may play a part in this. If the sensor is reporting incorrect values, this could affect drivability. Suggest using an ODB2 scanner to monitor the IAT and see if it is reasonable.

Check for vacuum leaks. Even the smallest leak will cause poor drivability. Check all hoses, PCV lines, intake tube, joints, connector, oil dip stick, valve cover gaskets, throttle body, intake gaskets, and evaporative purge lines. Today’s cars simply will not run well with a vacuum leak.

Next, check your spark plugs. Are they old? If so, change them. Also look for moisture in the spark plug wells. Be sure to thoroughly clean any debris from the spark plug wells before removing the plugs. Otherwise any debris is going straight into the combustion chamber.

What is the condition of the spark plug wires? All coil pack cars are 12+ years old. Coil packs fire on every stoke and are harder on wires. At minimum perform a visual inspection of the wires looking for evidence of arching/burning. Consider an old racer tick of running the car in the dark looking for the blue arc. The test is not always conclusive. Plug wires can still be bad.

Another thing to consider is replacing the front O2 sensors if more than 100k miles. As O2 sensors age, their response time slows. This slows the PCM’s ability to turn for changing conditions. Fuel mileage will suffer.

What about the condition of the Thermostat? If not closing completely, this will increase the time it takes for the motor to warm up.

Recommend starting with cleaning the MAF and checking for vacuum leaks.

Has it been doing this for a while or just recently?

Is it really, really, really cold where you are?

I think you solved your own problem. You need to let the car warm up to operating temp. before driving. You can get in and go, it will hesitate. Mine did the same thing, until i would go and start my car for 1 to 3 minutes before i leave.

I'm thinking vacum leak too, I think the hesitation would be the computer readjusting to too little vacum, would cause a drop in RPMs then it would bounce back, it might consider this normal in the drive cycle. Check your hoses and Pvc system for leaks, I would use a butane lighter and watch and listen for rise in rpms when you go by the leak.