sounds like a break in the wiring. cold contracts the connection and heat expands.
did you check all the grounds?
also next time there is a no start outside, get someone to be at the key while you do the wiggle test, start moving and wiggling some of the wires you can see and get at and go from there.
also check fuel pump circuit/relay, and tap the bottom of the tank to see if anything changes.
way back in the day we had an EFI ford pick up that wouldn`t start when it sat overnight in the cold, it was the fuel pump...
you`ll just have to start somewhere and keep checking things out... good luck.
do you hear the fuel pump prime when you first turn the key?