When outside temp is cold the truck cranks but will hesitate?

Cold weather-Okay you need to check the battery cold cranking amps could be low for your electrical system.

And also have the coolant temperature sensor check this one tells the computer to dump fuel at it, during initial cold starts-like a carbuerator choke till the engine comes up to its operating temperature then the oxygen sensor/s will take over the air/fuel mixture telling the computer whether it needs fuel or not.

It sounds like a weak fuel pump but to be sure you can do a fuel pump pressure test. Here is a guide to help you.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Fuel pump pressure should be 48 psi.

this guide may help as well

https://www.2carpros.com/articles/engine-cranks-excessively-before-starting

Here is how to change the pump out. Also, check the fuel pressure regulator by pulling the vacuum line off and if there is fuel present the regulator is bad and needs replacement. Check out the images (below). Please let us know what happens.