Did you try retorquing your conector tubes? Your obviously loosing pressure somewhere. In colder temperatures your cranking speed slows down just enough to not build the minimum pressure your computer needs to see before it will fire the injectors. Even if your starter was worn out and not cranking as quick as it should, it should still start. Warmer temperatures or using either (not recommended) will allow your motor to crank faster thus building more rail pressure, then she'll start.
You're truck is doing the EXACT same thing my 03 did. I got a shop to change all injectors AND conector tubes and problem went away.