If it is a dirty bottom most fuel filter submerged in the tank causing sudden cavitation,
then on a very cold winter day the truck will run for a longer time before suddenly dying
because the gasoline started cold and gradually warms up as fuel recirculation happens.

If it is an electrical fault
like a cracked wire killing power to the PCM due to vibration,
road jolts,
or warming up copper conductors,
then hot versus cold weather will have little effect on time run before dying.

If a fuel pressure gauge is plumbed in the pressure will show within normal range, then very suddenly drop to near zero psi.

If I were troubleshooting the truck’s problem I would be convinced by now that I needed an electrical multimeter that could record maximum and minimum voltages and currents, plus a fuel pressure sensor that this recording multimeter could be hooked to.

If you are REALLY intent on fixing this Dakota,
perhaps you should buy/borrow a same year Dakota and just begin swapping parts?

Tackling the recording multimeter methods with a fuel pressure sensor would eventually find the problem
but you have to be willing to learn how to use that equipment.
Once you learn those electrical tricks you can use them to fix vast numbers of things.