My 1999 Chevy S10 4.3L won't start in the cold with a brand new battery and alternator. This only happens in 10 degrees(F) or below. What could be the issue?

Question edited for clarity.
Question moved to correct model category.

You need an auto electrician with a pro grade scan tool computer to diagnose the charging circuit and battery drain.

https://www.google.com/search?q=auto+electrician+near+me

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can be several things. Like ice in a relay, oxidised contact, having a too high resistance in the cold. Low capacity of the battery. It is different for the battery, to deliver less then 1 amp for a radio, or 150 amps for the starter. Just pick up the multi meter and start checking voltages on different places in the start circuit.

try locking your car with the key and unlocking it with the key, leave it for 30 second or so between the locking and unlocking , the car thinks some one has tampered with it

CHECK THE MAIN FUSES, ON THE FRONT,, AND THE BATTERY CABLE.... YOU CAN REQUEST A SERVICE REPAIR MANUAL FOR FREE AT BESTDIRECTORYSOLUTIONS.COM

Car not starting or turning over indicates towards multiple possibilities. It can be issue with battery or weak battery. But if battery checks out ok, then it can be starter issue or faulty alternator or problem with low fuel pressure or no spark at spark plugs due to dirty spark plugs or faulty ignition coil or injectors getting cracked or dirty and needs to be cleaned.

To confirm the problem, the basic troubleshooting is required.

Click this link below and follow the troubleshooting:------

http://technoanswers.blogspot.in/2012/02/car-starting-issues.html

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This will help.

Thanks.

Is the battery goind dead while the vehicle is sitting and just won't start? Or is it dying while you are driving it?

Most possible that there is a heavy LEAK on the circuit and thus drains the circuit. This must be probed using a series ammeter which must be able to isolate the drain circuit when the main switch is OFF.
please check on the link below for tips:

http://www.fixya.com/cars/r5824824-draining_car_battery_charge

might be a bad crank sensor-they go bad all the time on Fords (4.6, right?)-unplug it, and plug it back in again, it might start right up, worth a try.

Check your battery cable ground and starter connections, and be sure battery post cable connections are clean and tight. If they all check out, change starter solenoid, or starter.

CHECK BATTERY WITH A LOAD TESTER,CHECK CABLE CONNECTIONS,AN STARTER . TRY JUMPING WITH A BOOSTER PAK THAT SHOULD START IT IF NOT REPLACE STARTER.