Not starting up in cold weather

[SeeKup]

I have a 2002 Explorer Sport (2dr) with auto 2wd and 115k miles. I live in Atlanta where it gets a little chilly (20s and 30s) and for the past 2 winters I've had trouble trying to start my car up. When it warms up toward the end of the day the car starts up fine. During the summer in the heat it starts up fine also, it's only when it gets around 40 degrees. I go through the same routine every morning which takes about 10 to 15 minutes which includes pressing the gas 1/2 way in and turning the key. It sounds like the car is about to turn over but doesn't start up. Last winter I flushed and replaced coolant and replaced the battery. I went to get the battery tested yesterday and turns out it was ok. The guys at AutoZone just told me it was a "thing with Fords" and there was nothing I could do about it. Frankly, I'm getting tired of waking up the neighborhood at 6:30 am every morning trying to start my car up.

TIA for any suggestions!

 

[SeeKup]

I went to the auto store and got my battery/alternator/starter tested and here are the results:

Battery: Good
Alternator: No problems
Starter: low cranking amps
"starter amp draw is low with ok starter voltage. Check starter circuit for loose, worn or corroded wiring."

Should I just replace the whole starter or is there a way to replace parts?