The most common reason for a car not starting, on a cold day, is the battery needs to be charged. Make sure the battery has a full charge.
Sounds like a starter or battery problem, possibly wiring problem
Oil slow getting to the head
its too cold
If your 2002 Ford Sport Trac is making a chirping noise when you do a cold start up, this could mean that you have a problem with the engine. You should have it looked at by a mechanic.
Most probably the noise is piston slap, this noise is heard when the engine is cold and disappears when the engine is hot. if the slap is very strong when the engine is cold and the noise becomes less when hot but still the noise can be heard.
It really depends on the cause of the noise. Every Inline-4 Cylinder car I have ever seen makes some kind of clicking type noise when they are started cold, I'm pretty sure it's noise from the mechanical valve lifters. If it's really concerning to you, take the car to a qualified mechanic.
A loose belt that becomes more noticeable at cold temperatures.
It could mean one of your timing belts are loose
If by stagering you mean hesitating or slow cranking , then you better check your battery and connections. Very hot or cold conditions require a lot of cranking power, if your battery is old I would have it checked out at your local Auto Zone or full service gas station.
different parts inside the gearbox will have driped dry and make more noise after starting from cold this noise should go away fairly quickly as the running gears move the oil around the gear box
check your belts they can be worn and need to be replaced or they just might be cold unless its everytime you start the car if that's the case the might need to be tightened your ac belt or fan belt could be bad.
check the oil