Ok. That's a clue. The alternator is running at full output trying to keep that battery going and you guys from getting stuck.
Like we said before, corroded or loose wires can cause this or it might just be time for a new battery.
If you have an advanced scan tool, you can pull up the state of charge. If it is below 65%, it's out of spec and needs replacement.
If you do not. Let the truck sit overnight and put a voltmeter on it in the morning. Compare the voltage with the outside temperature to get an idea of the state of charge according to this chart:
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